Datasets:

OpenCoder-LLM

/

opc-fineweb-math-corpus

like 19

Follow

OpenCoder 70

https://www.vn750.com/threads/front-wheel-not-aligned-with-handlebars.16804/

math

I bought my bike after it was layed down. Im not sure how hard it hit but it must have had some force when it did, it bent the brake lever and the right foot peg mount amoung other things. Now the front wheel isnt lined up with the handlebars, when the bars are straigt forward the wheel is slightly to the left. Upon further inspection i realized that the top of the right fork is even with the top of the upper triple tree, but the top of the left fork is slightly higher than the tree. Which one is correct? should the top of the fork be even with the tree? also, what would be the best way of re-aligning the wheel to the bars and the trees? Any help would be much appreciated.

s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655902496.52/warc/CC-MAIN-20200710015901-20200710045901-00039.warc.gz

CC-MAIN-2020-29

http://www.silmarillionwritersguild.org/archive/home/reviews.php?type=ST&item=809&chapid=3276

math

Home  |  Most Recent  |  Authors  |  Titles  |  Search  |  Series  |  Podfics  |  Top Tens  |  Login  |    | Comments For Character of the Month Biographies I know exact;y what you mean about thinking you've picked an easy/quick one to write and "seven hours later . . ." I'm forever doing that. You found some good stuff though. It was worth the effort. Hello! Thank you for bringing together facts of one of my fav intriguing characters, whi should be there, but are just mentioned. Or maybe he is one of my fav for being so blank card can be filled with whatever I want ;) Which reminds me I haven't checked how is your Ingwë for ages, got to check stories one day. Your Aman is not my Aman, but is a fascinating place to read about. Cheers! Thanks. I've posted a few new chapters of the Valinor story in recent months, and though Ingwe hasn't appeared yet, he will be showing up soon. Oh, brilliant! Ingwë is one of those characters I remembered ever so vaguely, and I was struggling to piece together who was who in your current WIP. So it comes at a great time (probably no coincidence...). Not for the first time, it's "a great wonderment to me" that another fascinating character gets edited out or pared to the bone in the published version of the Silmarillion, so it's great that you have "rediscovered" him. "Teleri was the original clan name for the Vanyar. Those who later became known as the Teleri were at this time called the Solosimpi." Thanks for including that note, for a moment I thought I had amnesia. Thank you, Darth! EDIT: It keeps posting the review in the wrong place, it is meant to go under the Ingwë bio. Hmm, yeah, I should probably admit to a certain self-serving interest in writing this. I actually came across a number of interesting and previously unknown facts about Ingwe in particular and Vanyar in general, all of which will be worked into the Damn Valinor Story. Thanks! This is great: a character that I for one know very little about. So glad to have the information handy. I thought this would be an easy bio to write, since I was under the impression that there was little to know about Ingwe in general. Seven hours later...

s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891377.59/warc/CC-MAIN-20180122133636-20180122153636-00485.warc.gz

CC-MAIN-2018-05

https://www.hiattthai.com/product/57675-54448/variable-primary-pressure-flow-controller-model-2204-series

math

Model 2204 Variable Primary Pressure Flow Controller is a control valve that always keeps flows at a constant rate under a given constant level of secondary pressure (outlet pressure) even when the primary pressure (inlet pressure) fluctuates. The built-in precision needle valve accurately controls flows to the set flow rate, including ultra-minute flows. • Stable flow control A non-rotary needle valve composed of high-precision components ensures smooth control of even ultra-minute flows. • Not subject to supply pressure fluctuations Flows are protected from being affected by primary pressure (supply pressure) fluctuations, under a given constant level of secondary pressure (outlet pressure). • Cleanliness ensured All the high-precision components are super-cleaned before assembly so that the product can be safely used even on high-sensitivity instruments for analysis for which cleanliness is essential. • Physical and chemical appliances • Control of the second-stage operation of pumps • Various instruments for analysis • Environmental instrumentation systems

s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947475757.50/warc/CC-MAIN-20240302052634-20240302082634-00066.warc.gz

CC-MAIN-2024-10

http://tedmcginley.com/read/introduction-to-classical-mechanics

math

Download Introduction to Classical Mechanics by David Morin PDF By David Morin This textbook covers all of the commonplace introductory themes in classical mechanics, together with Newton's legislation, oscillations, strength, momentum, angular momentum, planetary movement, and specific relativity. It additionally explores extra complicated issues, equivalent to general modes, the Lagrangian strategy, gyroscopic movement, fictitious forces, 4-vectors, and normal relativity. It comprises greater than 250 issues of unique ideas so scholars can simply payment their knowing of the subject. There also are over 350 unworked routines that are excellent for homework assignments. Password safe options can be found to teachers at www.cambridge.org/9780521876223. The enormous variety of difficulties on my own makes it an amazing supplementary textual content for all degrees of undergraduate physics classes in classical mechanics. feedback are scattered through the textual content, discussing matters which are usually glossed over in different textbooks, and it really is completely illustrated with greater than six hundred figures to assist reveal key strategies. Read Online or Download Introduction to Classical Mechanics PDF Best mechanics books Includes the elemental idea of mechanics and symmetry. Designed to strengthen the fundamental concept and functions of mechanics with an emphasis at the function of symmetry. Quantitative equipment have a selected knack for making improvements to any box they contact. For biology, computational strategies have ended in huge, immense strides in our knowing of organic platforms, yet there's nonetheless substantial territory to hide. Statistical physics particularly holds nice power for elucidating the structural-functional relationships in biomolecules, in addition to their static and dynamic homes. The mechanics of electromagnetic fabrics and buildings has been constructing speedily with vast functions in, e. g. , electronics undefined, nuclear engineering, and clever fabrics and buildings. Researchers during this interdisciplinary box are with diversified heritage and motivation. The Symposium at the Mechanics of Electromagnetic fabrics and constructions of the Fourth foreign convention on Nonlinear Mechanics in Shanghai, China in August 13-16, 2002 supplied a chance for an intimate amassing of researchers and trade of rules. This detailed textbook goals to introduce readers to the fundamental buildings of the mechanics of deformable our bodies, with a distinct emphasis at the description of the elastic habit of easy fabrics and constructions composed via elastic beams. The authors take a deductive instead of inductive process and begin from a number of first, foundational ideas. - Mechanics and Energetics of Biological Transport - Radiation Damage. Behaviour of Insonated Metals: Course Held at the Department for Mechanics of Deformable Bodies October 1970 - Classical mechanics : transformations, flows, integrable, and chaotic dynamics - Topics in dynamics I: Flows - Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition Additional resources for Introduction to Classical Mechanics Balancing the stick Let the stick go off to infinity in the positive x direction, and let it be cut at x = x0 . Then the pivot point is located at x = x0 + (see Fig. 55). Let the density be ρ(x). The condition that the total gravitational torque relative to x0 + equal zero is ∞ τ= ρ(x) x − (x0 + ) g dx = 0. 55 I-30 CHAPTER 1. STATICS We want this to equal zero for all x0 , so the derivative of τ with respect to x0 must be zero. τ depends on x0 through both the limits of integration and the integrand. 51) This is the desired equation that determines α. Given d, λ, and , we can numerically solve for α. Using a “half-angle” formula, you can show that eq. 51) may also be written as 2 sinh(αd/2) = α 2 − λ2 . 52) Remark: Let’s check a couple limits. If λ = 0 and = d (that is, the chain forms a horizontal straight line), then eq. 52) becomes 2 sinh(αd/2) = αd. The solution to this is α = 0, which does indeed correspond to a horizontal straight line, because for small α, eq. 47) behaves like αx2 /2 (up to an additive constant), which varies slowly with x for small α. We’ll do the following example by putting the initial conditions in the limits of integration. 12 The drag force is roughly proportional to v as long as the speed is fairly slow. For large speeds, the drag force is roughly proportional to v 2 . II-12 CHAPTER 2. USING F = M A Therefore, y(t) = h − g α t− 1 1 − e−αt α . 33) Remarks: (a) Let’s look at some limiting cases. If t is very small (more precisely, if αt 1), then we can use e−x ≈ 1 − x + x2 /2 to make approximations to leading order in t.

s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247479729.27/warc/CC-MAIN-20190216004609-20190216030609-00439.warc.gz

CC-MAIN-2019-09

http://laundrylynx.com/epub/basic-college-mathematics-a-real-world-approach

math

By Ignacio Bello Easy university arithmetic should be a evaluation of primary math recommendations for a few scholars and will holiday new flooring for others. however, scholars of all backgrounds could be extremely joyful to discover a clean publication that appeals to all studying types and reaches out to assorted demographics. via down-to-earth reasons, sufferer skill-building, and enormously fascinating and real looking purposes, this worktext will empower scholars to profit and grasp arithmetic within the genuine global. Read or Download Basic College Mathematics: A Real-World Approach PDF Similar popular & elementary books The speculation of persevered fractions has been outlined by means of a small handful of books. this is often considered one of them. the focal point of Wall's publication is at the learn of endured fractions within the concept of analytic services, instead of on arithmetical facets. There are prolonged discussions of orthogonal polynomials, strength sequence, countless matrices and quadratic types in infinitely many variables, yes integrals, the instant challenge and the summation of divergent sequence. Written and revised via D. B. A. Epstein. Common geometry offers the basis of contemporary geometry. For the main half, the normal introductions finish on the formal Euclidean geometry of highschool. Agricola and Friedrich revisit geometry, yet from the better standpoint of collage arithmetic. aircraft geometry is built from its simple items and their houses after which strikes to conics and uncomplicated solids, together with the Platonic solids and an evidence of Euler's polytope formulation. - High Performance Computing in Remote Sensing (Chapman & Hall Crc Computer & Information Science Series) - Infinite Electrical Networks - Scientific Computing with Multicore and Accelerators - The Essentials of Pre-Calculus - Arithmetic, Proof Theory, and Computational Complexity Additional info for Basic College Mathematics: A Real-World Approach 0ϩ1ϭ1 Step 3. 410,000 ︸ Change to zeros Thus, 405,648 rounded to the nearest ten thousand is 410,000. Rounding whole numbers This year, the best-selling car in America is the Toyota Camry. Use the chart to round the specified prices. Suppose you have a $22,000 budget. PROBLEM 7 a. Round the True Market Value (TMV) Base Price to the nearest hundred. b. Round the TMV price of the GJ package #3 to the nearest hundred. c. Round the TMV price of the BE package to the nearest hundred. a. the GU package. You should be able to: Find the place value of a digit in a numeral. (p. 3) AV Determine if a given number is less than or greater than another number. BV Round whole numbers to the specified place value. CV Solve applications involving the concepts studied. indd 13 V Getting Started How long is a large paper clip? To the nearest inch, it is 2 inches. 12/11/07 9:59:18 AM 14 Chapter 1 1-14 Whole Numbers A V Ordering Numbers We know that 2 is greater than one because the 2 on the ruler is to the right of the one. Write the numeral 173,880 in words. 72. Germs on your phone The average phone has 25,127 germs per square inch. Write the numeral 25,127 in words. Source: Microbiologist Charles Gerba. 73. School attendance On an average day in America, 13,537,000 students attend secondary school. Write the numeral 13,537,000 in words. 74. Rainfall on an acre A rainfall of 1 inch on an acre of ground will produce six million, two hundred seventy-two thousand, six hundred forty cubic inches of water. Write this number in standard form. Basic College Mathematics: A Real-World Approach by Ignacio Bello

s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249508792.98/warc/CC-MAIN-20190223162938-20190223184938-00636.warc.gz

CC-MAIN-2019-09

http://www.expertsmind.com/questions/effect-of-changing-supply-on-total-revenue-30134921.aspx

math

Problem: Elasticity, Total Revenue and Marginal Revenue For Each of the following cases, what is the expected impact on the total revenue of the firm? Explain your reasoning (a) Price elasticity of demand is known to be 0:5 and the firm raises price by 10%. (b) Price elasticity of demand is known to be 2:5 and the firm lowers price by 5%. (c) Price elasticity of demand is known to be 1:0 and the firm raises price by 1%. Suppose the demand equation for good x was estimated as QxD = 500 - 2Px: (a) What is the price at which total revenue is maximized and what is the value of the total revenue at this point. Illustrate graphically. (b) Identify the elastic and the inelastic ranges on the demand curve. Problem : Effect of changing supply on total revenue (4 points) Farm stories for July 26th, 2007. Written by Jim Birchard, Bayshore Broadcasting Corp. The largest winter wheat crop ever produced in Western Canada is set to begin harvesting this week. The Canadian Wheat Board says the 1.45 million acres seeded to the crop will yield record production. Winter-wheat yields are on track to match or surpass last yearís record-setting yield results. Based on the above excerpt, would you expect the income of the wheat farmers to increase or decrease? Explain with a demand-supply diagram.

s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123530.18/warc/CC-MAIN-20170423031203-00235-ip-10-145-167-34.ec2.internal.warc.gz

CC-MAIN-2017-17

https://www.qub.ac.uk/schools/SchoolofMathematicsandPhysics/Discover/Outreach/GirlsinMathsandPhysics/

math

Girls in Maths and Physics Girls in Maths and Physics is an event to inspire young female mathematicians and their teachers. Bringing together inspirational speakers, fun activities and real life working mathematicians and physicists, this event is targeted at girls aged 12-16 who have an interest in mathematics, physics and their applications. In June 2022, we were delighted to welcome Professor Colm Mulcahy, from Spelman College in Atlanta, as our keynote speaker. Colm runs the Annals of Irish Mathematics & Mathematicians (AIMM) website (www.mathsireland.ie) which aims to document all Irish students who earned advanced mathematics degrees. Colm’s talk, entitled "Pioneering Women in Irish Maths & Physics", highlighted Irish women who have made significant contributions to pure and applied maths and mathematical physics from the 1860s to the present day. Girls in Maths and Physics is sponsored by Queen's School of Mathematics and Physics and the Athena SWAN Initiative. Details of the 2023 event will be published here soon.

s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945440.67/warc/CC-MAIN-20230326075911-20230326105911-00452.warc.gz

CC-MAIN-2023-14

http://forums.wolfram.com/mathgroup/archive/2004/Jun/msg00297.html

math

exporting the values of evaluated functions - To: mathgroup at smc.vnet.net - Subject: [mg48773] exporting the values of evaluated functions - From: Feleki Zsolt <felke2000 at yahoo.com> - Date: Wed, 16 Jun 2004 04:54:20 -0400 (EDT) - Sender: owner-wri-mathgroup at wolfram.com I have a complicated function defined by the integration of another function. Plotting the former function using Evaluate is no problem, but it is not possible to see or export the values of the function explicitly. Since Mathematica plots the function, it surely has to calculate it, so I am sure there must be a way to see also the values that he calculates. Bye, Zsolt Feleki Hochbautechnik/ Professur für Bauphysik Do you Yahoo!? Read only the mail you want - Yahoo! Mail SpamGuard. Prev by Date: Re: I have sounds in Mathematica -> want sound files Next by Date: SOLVING A CUBE Previous by thread: Re: How to modify Convex Hull program to give output as Cartesian Coordinates? Next by thread: Re: exporting the values of evaluated functions

s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323680.18/warc/CC-MAIN-20170628120308-20170628140308-00097.warc.gz

CC-MAIN-2017-26

http://mathhelpforum.com/math-puzzles/168146-addition-subtraction-puzzle-calculus-print.html

math

The addition-subtraction puzzle (calculus) In my easy calculus puzzle, I've submitted (in another form) and I pointed out how by letting 1 = would lead to a solution. The formula can be rewritten as 1 = for the numerator of the first fraction which of course leads to the same answer. That method I refer to as the addition-subtraction method or ASM for short (which is applied to the numerators of fractions). This is a method that should be taught in calculus classes and demonstrated in texts, but unfortunately isn't. It's a powerful method for simplifying fractions and I'll now give you another example in the form of an easy puzzle. Using ASM, transform into two fractions and then go on to integrate those two fractions.

s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118743.41/warc/CC-MAIN-20170423031158-00626-ip-10-145-167-34.ec2.internal.warc.gz

CC-MAIN-2017-17

https://www.oreilly.com/library/view/advanced-engineering-mathematics/9780470458365/Chapter014.html

math

Chapter 13 laid the groundwork for the study of complex analysis, covered complex numbers in the complex plane, limits, and differentiation, and introduced the most important concept of analyticity. A complex function is analytic in some domain if it is differentiable in that domain. Complex analysis deals with such functions and their applications. The Cauchy–Riemann equations, in Sec. 13.4, were the heart of Chapter 13 and allowed a means of checking whether a function is indeed analytic. In that section, we also saw that analytic functions satisfy Laplace's equation, the most important PDE in physics. We now consider the next part of complex calculus, that is, we shall discuss the first approach to complex integration. It centers around the very important Cauchy integral theorem (also called the Cauchy–Goursat theorem) in Sec. 14.2. This theorem is important because it allows, through its implied Cauchy integral formula of Sec. 14.3, the evaluation of integrals having an analytic integrand. Furthermore, the Cauchy integral formula shows the surprising result that analytic functions have derivatives of all orders. Hence, in this respect, complex analytic functions behave much more simply than real-valued functions of real variables, which may have derivatives only up to a certain order. Complex integration is attractive for several reasons. Some basic properties ...

s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988759.29/warc/CC-MAIN-20210506175146-20210506205146-00221.warc.gz

CC-MAIN-2021-21

https://www.hindawi.com/journals/ijap/2013/261230/

math

Advances in Antenna Array Processing for RadarView this Special Issue Array Processing for Radar: Achievements and Challenges Array processing for radar is well established in the literature, but only few of these algorithms have been implemented in real systems. The reason may be that the impact of these algorithms on the overall system must be well understood. For a successful implementation of array processing methods exploiting the full potential, the desired radar task has to be considered and all processing necessary for this task has to be eventually adapted. In this tutorial paper, we point out several viewpoints which are relevant in this context: the restrictions and the potential provided by different array configurations, the predictability of the transmission function of the array, the constraints for adaptive beamforming, the inclusion of monopulse, detection and tracking into the adaptive beamforming concept, and the assessment of superresolution methods with respect to their application in a radar system. The problems and achieved results are illustrated by examples from previous publications. Array processing is well established for radar. Publications of this topic have appeared for decades, and one might question what kind of advances we may still expect now. On the other hand, if we look at existing radar systems we will find very few methods implemented from the many ideas discussed in the literature. The reason may be that all processing elements of a radar system are linked, and it is not very useful to simply implement an isolated algorithm. The performance and the property of any algorithm will have an influence on the subsequent processing steps and on the radar operational modes. Predictability of the system performance with the new algorithms is a key issue for the radar designer. Advanced array processing for radar will therefore require to take these interrelationships into account and to adapt the related processing in order to achieve the maximum possible improvement. The standard handbooks on radar [1, 2] do not mention this problem. The book of Wirth is an exception and mentions a number of the array processing techniques described below. In this tutorial paper, viewpoints are presented which are relevant for the implementation of array processing methods. We do not present any new sophisticated algorithms, but for the established algorithms we give examples of the relations between array processing and preceding and subsequent radar processing. We point out the problems that have to be encountered and the solutions that need to be developed. We start with spatial sampling, that is, the antenna array that has to be designed to fulfill all requirements of the radar system. A modern radar is typically a multitasking system. So, the design of the array antenna has to fulfill multiple purposes in a compromise. In Section 3, we briefly review the approaches for deterministic pattern shaping which is the standard approach of antenna-based interference mitigation. It has the advantage of requiring little knowledge about the interference scenario, but very precise knowledge about the array transfer function (“the array manifold”). Adaptive beamforming (ABF) is presented in Section 4. This approach requires little knowledge about the array manifold but needs to estimate the interference scenario from some training data. Superresolution for best resolution of multiple targets is sometimes also subsumed under adaptive beamforming as it resolves everything, interference and targets. These methods are considered in Section 5. We consider superresolution methods here solely for the purpose of improved parameter estimation. In Section 6, we briefly mention the canonical extension of ABF and superresolution to space-time array processing. Section 7 is the final and most important contribution. Here we point out how direction estimation must be modified if adaptive beams are used, and how the radar detector, the tracking algorithm, and the track management should be adapted for ABF. 2. Design Factors for Arrays Array processing starts with the array antenna. This is hardware and is a selected construction that cannot be altered. It must therefore be carefully designed to fulfill all requirements. Digital array processing requires digital array outputs. The number and quality of these receivers (e.g., linearity and number of ADC bits) determine the quality and the cost of the whole system. It may be desirable to design a fully digital array with AD-converters at each antenna element. However, weight and cost will often lead to a system with reduced number of digital receivers. On the other hand, because of the -decay of the received power, radar needs antennas with high gain and high directional discrimination, which means arrays with many elements. There are different solutions to solve this contradiction.(i)Thinned arrays: the angular discrimination of an array with a number of elements can be improved by increasing the separation of the elements and thus increasing the aperture of the antenna. Note that the thinned array has the same gain as the corresponding fully filled array.(ii)Subarrays: element outputs are summed up in an analog manner into subarrays which are then AD-converted and processed digitally. The size and the shape of the subarrays are an important design criterion. The notion of an array with subarrays is very general and includes the case of steerable directional array elements. 2.1. Impact of the Dimensionality of the Array Antenna elements may be arranged on a line (1-dimensional array), on a plane (a ring or a 2-dimensional planar array), on a curved surface (conformal array), or within a volume (3D-array, also called Crow’s Nest antenna, [3, Section ]). A 1-dimensional array can only measure one independent angle; 2D and 3D arrays can measure the full polar coordinates in . Antenna element design and the need for fixing elements mechanically lead to element patterns which are never omnidirectional. The elements have to be designed with patterns that allow a unique identification of the direction. Typically, a planar array can only observe a hemispherical half space. To achieve full spherical coverage, several planar arrays can be combined (multifacetted array), or a conformal or volume array may be used. 2.1.1. Arrays with Equal Patterns For linear, planar, and volume arrays, elements with nearly equal patterns can be realized. These have the advantage that the knowledge of the element pattern is for many array processing methods not necessary. An equal complex value can be interpreted as a modified target complex amplitude, which is often a nuisance parameter. More important is that, if the element patterns are really absolutely equal, any cross-polar components of the signal are in all channels equal and fulfill the array model in the same way as the copolar components; that is, they produce no error effect. 2.1.2. Arrays with Unequal Array Patterns This occurs typically by tilting the antenna elements as is done for conformal arrays. For a planar array, this tilt may be used to realize an array with polarization diversity. Single polarized elements are then mounted with orthogonal alignment at different positions. Such an array can provide some degree of dual polarization reception with single channel receivers (contrary to more costly fully polarimetric arrays with receivers for both polarizations for each channel). Common to arrays with unequal patterns is that we have to know the element patterns for applying array processing methods. The full element pattern function is also called the array manifold. In particular, the cross-polar (or short -pol) component has a different influence for each element. This means that if this component is not known and if the -pol component is not sufficiently attenuated, it can be a significant source of error. 2.2. Thinned Arrays To save the cost of receiving modules, sparse arrays are considered, that is, with fewer elements than the full populated grid. Because such a “thinned array” spans the same aperture, it has the same beamwidth. Hence, the angular accuracy and resolution are the same as the fully filled array. Due to the gaps, ambiguities or at least high sidelobes may arise. In early publications like , it was advocated to simply take out elements of the fully filled array. It was early recognized that this kind of thinning does not imply “sufficiently random” positions. Random positions on a grid as used in [3, Chapter 17] can provide quite acceptable patterns. Note that the array gain of a thinned array with elements is always , and the average sidelobe level is . Today, we know from the theory of compressed sensing that a selection of sufficiently random positions can produce a unique reconstruction of a not too large number of impinging wave fields with high probability . 2.3. Arrays with Subarrays If a high antenna gain with low sidelobes is desired one has to go back to the fully filled array. For large arrays with thousands of elements, the large number of digital channel constitutes a significant cost factor and a challenge for the resulting data rate. Therefore, often subarrays are formed, and all digital (adaptive) beamforming and sophisticated array processing methods are applied to the subarray outputs. Subarraying is a very general concept. At the elements, we may have phase shifters such that all subarrays are steered into a given direction and we may apply some attenuation (tapering) to influence the sidelobe level. The sum of the subarrays then gives the sum beam output. The subarrays can be viewed as a superarray with elements having different patterns steered into the selected direction. The subarrays should have unequal size and shape to avoid grating effects for subsequent array processing, because the subarray centers constitute a sparse array (for details, see ). The principle is indicated in Figure 1, and properties and options are described in [6, 7]. In particular, one can also combine new subarrays at the digital level or distribute the desired tapering over the analog level and various digital levels . Beamforming using subarrays can be mathematically described by a simple matrix operation. Let the complex array element outputs be denoted by . The subarray forming operation is described by a subarray forming matrix by which the element outputs are summed up as . For subarrays and antenna elements, is of size . Vectors and matrices at the subarray outputs are denoted by the tilde. Suppose we steer the array into a look direction by applying phase shifts and apply additional amplitude weighting at the elements (real vector of length ) for a sum beam with low sidelobes, then we have a complex weighting which can be included in the elements of the matrix . Here, denotes the centre frequency, , denote the coordinates of the th array element, denotes the velocity of light, and , denote the components of the unit direction vector in the planar antenna -coordinate system. The beams are formed digitally with the subarray outputs by applying a final weighting as In the simplest case, consists of only ones. The antenna pattern of such a sum beam can then be written as where and denotes the plane wave response at the subarray outputs. All kinds of beams (sum, azimuth and elevation difference, guard channel, etc.) can be formed from these subarray outputs. We can also scan the beam digitally at subarray level into another direction, . Figure 2 shows a typical planar array with 902 elements on a triangular grid with 32 subarrays. The shape of the subarrays was optimized by the technique of such that the difference beams have low sidelobes when a −40 dB Taylor weighting is applied at the elements. We will use this array in the sequel for presenting examples. An important feature of digital beamforming with subarrays is that the weighting for beamforming can be distributed between the element level (the weighting incorporated in the matrix ) and the digital subarray level (the weighting ). This yields some freedom in designing the dynamic range of amplifiers at the elements and the level of the AD-converter input. This freedom also allows to normalize the power of the subarray outputs such that . As will be shown in Section 4, this is also a reasonable requirement for adaptive interference suppression to avoid pattern distortions. 2.4. Space-Time Arrays Coherent processing of a time series can be written as a beamforming procedure as in (1). For a time series of array snapshots , we have therefore a double beamforming procedure of the space-time data matrix of the form where , denote the weight vectors for spatial and temporal beamforming, respectively. Using the rule of Kronecker products, (3) can be written as a single beamforming operation where is a vector obtained by stacking all columns of the matrix on top. This shows that mathematically it does not matter whether the data come from spatial or temporal sampling. Coherent processing is in both cases a beamforming-type operation with the correspondingly modified beamforming vector. Relation (4) is often exploited when spatial and temporal parameters are dependent (e.g., direction and Doppler frequency as in airborne radar; see Section 6). 3. Antenna Pattern Shaping Conventional beamforming is the same as coherent integration of the spatially sampled data; that is, the phase differences of a plane wave signal at the array elements are compensated, and all elements are coherently summed up. This results in a pronounced main beam when the phase differences match with the direction of the plane wave and result in sidelobes otherwise. The beam shape and the sidelobes can be influenced by additional amplitude weighting. Let us consider the complex beamforming weights , . The simplest way of pattern shaping is to impose some bell-shaped amplitude weighting over the aperture like (for suitable constants , ), or . The foundation of these weightings is quite heuristical. The Taylor weighting is optimized in the sense that it leaves the conventional (uniformly weighted) pattern undistorted except for a reduction of the first sidelobes below a prescribed level. The Dolph-Chebyshev weighting creates a pattern with all sidelobes equal to a prescribed level. Figure 3 shows examples of such patterns for a uniform linear array with 40 elements. The taper functions for low sidelobes were selected such that the 3 dB beamwidth of all patterns is equal. The conventional pattern is plotted for reference showing how tapering increases the beamwidth. Which of these taperings may be preferred depends on the emphasis on close in and far off sidelobes. Another point of interest is the dynamic range of the weights and the SNR loss, because at the array elements only attenuations can be applied. One can see that the Taylor tapering has the smallest dynamic range. For planar arrays the efficiency of the taperings is slightly different. (a) Low sidelobe patterns of equal beamwidth (b) Taper functions for low sidelobes The rationale for low sidelobes is that we want to minimize some unknown interference power coming over the sidelobes. This can be achieved by solving the following optimization problem, : denotes the angular sector where we want to influence the pattern, for example, the whole visible region , and is a weighting function which allows to put different emphasis on the criterion in different angular regions. The solution of this optimization is For the choice of the function , we remark that for a global reduction of the sidelobes when , one should exclude the main beam from the minimization by setting on this set of directions (in fact, a slightly larger region is recommended, e.g., the null-to-null width) to allow a certain mainbeam broadening. One may also form discrete nulls in directions by setting . The solution of (5) then can be shown to be This is just the weight for deterministic nulling. To avoid insufficient suppression due to channel inaccuracies, one may also create small extended nulls using the matrix . The form of these weights shows the close relationship to the adaptive beamforming weights in (11) and (17). An example for reducing the sidelobes in selected areas where interference is expected is shown in Figure 4. This is an application from an airborne radar where the sidelobes in the negative elevation space have been lowered to reduce ground clutter. 4. Adaptive Interference Suppression Deterministic pattern shaping is applied if we have rough knowledge about the interference angular distribution. In the sidelobe region, this method can be inefficient because the antenna response to a plane wave (the vector ) must be exactly known which is in reality seldom the case. Typically, much more suppression is applied than necessary with the price paid by the related beam broadening and SNR loss. Adaptive interference suppression needs no knowledge of the directional behavior and suppresses the interference only as much as necessary. The proposition for this approach is that we are able to measure or learn in some way the adaptive beamforming (ABF) weights. In the sequel, we formulate the ABF algorithms for subarray outputs as described in (1). This includes element space ABF for subarrays containing only one element. 4.1. Adaptive Beamforming Algorithms Let us first suppose that we know the interference situation; that is, we know the interference covariance matrix . What is the optimum beamforming vector ? From the Likelihood Ratio test criterion, we know that the probability of detection is maximized if we choose the weight vector that maximizes the signal-to-noise-plus-interference ratio (SNIR) for a given (expected) signal , The solution of this optimization is is a free normalization constant and denotes interference and receiver noise. This weighting has a very intuitive interpretation. If we decompose and apply this weight to the data, we have . This reveals that ABF does nothing else but a pre-whiten and match operation: if contains only interference, that is, , then , the prewhitening operation; the operation of on the (matched) signal vector restores just the matching necessary with the distortion from the prewhitening operation. This formulation for weight vectors applied at the array elements can be easily extended to subarrays with digital outputs. As mentioned in Section 2.3, a subarrayed array can be viewed as a superarray with directive elements positioned at the centers of the subarrays. This means that we have only to replace the quantities , by , . However, there is a difference with respect to receiver noise. If the noise at the elements is white with covariance matrix it will be at subarray outputs with covariance matrix . Adaptive processing will turn this into white noise. Furthermore, if we apply at the elements some weighting for low sidelobes, which are contained in the matrix , ABF will reverse this operation by the pre-whiten and match principle and will distort the low sidelobe pattern. This can be avoided by normalizing the matrix such that . This can be achieved by normalizing the element weight as mentioned in Section 2.3 (for nonoverlapping subarrays). Sometimes interference suppression is realized by minimizing only the jamming power subject to additional constraints, for example, , for suitable vectors and numbers , . Although this is an intuitively reasonable criterion, it does not necessarily give the maximum SNIR. For certain constraints however both solutions are equivalent. The constrained optimization problem can be written in general terms as and it has the solution Examples of special cases are as follows:(i)Single unit gain directional constraint: . This is obviously equivalent to the SNIR-optimum solution (9) with a specific normalization.(ii)Gain and derivative constraint: , with suitable values of the Lagrange parameters , . A derivative constraint is added to make the weight less sensitive against mismatch of the steering direction.(iii)Gain and norm constraint: , . The norm constraint is added to make the weight numerically stable. This is equivalent to the famous diagonal loading technique which we will consider later.(iv)Norm constraint only: . Without a directional constraint the weight vector produces a nearly omnidirectional pattern, but with nulls in the interference directions. This is also called the power inversion weight, because the pattern displays the inverted interference power. As we mentioned before, fulfilling the constraints may imply a loss in SNIR. Therefore, several techniques have been proposed to mitigate the loss. The first idea is to allow a compromise between power minimization and constraints by introducing coupling factors and solve a soft constraint optimization with . The solution of the soft-constraint optimization is One may extend the constrained optimization by adding inequality constraints. This leads to additional and improved robustness properties. A number of methods of this kind have been proposed, for example, in [9–12]. As we are only presenting the principles here we do not go into further details. The performance of ABF is often displayed by the adapted antenna pattern. A typical adapted antenna pattern with 3 jammers of 20 dB SNR is shown in Figure 5(a) for generic array of Figure 2. This pattern does not show how the actual jamming power and the null depth play together. (a) Adapted antenna pattern Plots of the SNIR are better suited for displaying this effect. The SNIR is typically plotted for varying target direction while the interference scenario is held fixed, as seen in Figure 5(b). The SNIR is normalized to the SNR in the clear absence of any jamming and without ABF. In other words, this pattern shows the insertion loss arising from the jamming scenario with applied ABF. The effect of target and steering direction mismatch is not accounted for in the SNIR plot. This effect is displayed by the scan pattern, that is, the pattern that arises if the adapted beam scans over a fixed target and interference scenario. Such a plot is rarely shown because of the many parameters to be varied. In this context, we note that for the case that the training data contains the interference and noise alone the main beam of the adapted pattern is fairly broad similar to the unadapted sum beam and is therefore fairly insensitive to pointing mismatch. How to obtain an interference-alone covariance matrix is a matter of proper selection of the training data as mentioned in the following section. Figure 5 shows the case of an untapered planar antenna. The first sidelobes of the unadapted antenna pattern are at −17 dB and are nearly unaffected by the adaptation process. If we have an antenna with low sidelobes, the peak sidelobe level is much more affected; see Figure 6. Due to the tapering we have a loss in SNIR of 1.7 dB compared to the reference antenna (untapered without ABF and jamming). (a) Adapted antenna pattern 4.2. Estimation of Adaptive Weights In reality, the interference covariance matrix is not known and must be estimated from some training data . To avoid signal cancellation, the training data should only contain the interference alone. If we have a continuously emitting interference source (noise jammer) one may sample immediately after or before the transmit pulse (leading or rear dead zone). On the other hand, if we sample the training data before pulse compression the desired signal is typically much below the interference level, and signal cancellation is negligible. Other techniques are described in . The maximum likelihood estimate of the covariance matrix is then This is called the Sample Matrix Inversion algorithm (SMI). The SMI method is only asymptotically a good estimate. For small sample size, it is known to be not very stable. For matrix invertibility, we need at least samples. According to Brennan’s Rule, for example, , one needs samples to obtain an average loss in SNIR below 3 dB. For smaller sample size, the performance can be considerably worse. However, by simply adding a multiple of the identity matrix to the SMI estimate, a close to optimum performance can be achieved. This is called the loaded sample matrix estimate (LSMI) The drastic difference between SMI and LSMI is shown in Figure 7 for the planar array of Figure 2 for three jammers of 20 dB input JNR with 32 subarrays and only 32 data snapshots. For a “reasonable” choice of the loading factor (a rule of thumb is for an untapered antenna) we need only snapshots to obtain a 3 dB SNIR loss, if denotes the number of jammers (dominant eigenvalues) present, . So the sample size can be considerably lower than the dimension of the matrix. The effect of the loading factor is that the dynamic range of the small eigenvalues is compressed. The small eigenvalues possess the largest statistical fluctuation but have the greatest influence on the weight fluctuation due to the matrix inversion. One may go even further and ignore the small eigenvalue estimates completely; that is, one tries to find an estimate of the inverse covariance matrix based on the dominant eigenvectors and eigenvalues. For high SNR, we can replace the inverse covariance matrix by a projection matrix. Suppose we have jammers with amplitudes in directions . If the received data has the form , or short , then Here, we have normalized the noise power to 1 and . Using the matrix inversion lemma, we have is a projection on the space orthogonal to the columns of . For strong jammers, the space spanned by the columns of will be the same as the space spanned by the dominant eigenvectors. We may therefore replace the estimated inverse covariance matrix by a projection on the complement of the dominant eigenvectors. This is called the EVP method. As the eigenvectors are orthonormalized, the projection can be written as . Figure 7 shows the performance of the EVP method in comparison with SMI, LSMI. Note the little difference between LSMI and EVP. The results with the three methods are based on the same realization of the covariance estimate. For EVP, we have to know the dimension of the jammer subspace (dimJSS). In complicated scenarios and with channel errors present, this value can be difficult to determine. If dimJSS is grossly overestimated, a loss in SNIR occurs. If dimJSS is underestimated the jammers are not fully suppressed. One is therefore interested in subspace methods with low sensitivity against the choice of the subspace dimension. This property is achieved by a “weighted projection,” that is, by replacing the projection by where is a diagonal weighting matrix and is a set orthonormal vectors spanning the interference subspace. does not have the mathematical properties of a projection. Methods of this type of are called lean matrix inversion (LMI). A number of methods have been proposed that can be interpreted as an LMI method with different weighting matrices . The LMI matrix can also be economically calculated by an eigenvector-free QR-decomposition method, . One of the most efficient methods for pattern stabilization while maintaining a low desired sidelobe level is the constrained adaptive pattern synthesis (CAPS) algorithm, , which is also a subspace method. Let be the vector for beamforming with low sidelobes in a certain direction. In full generality, the CAPS weight can be written as where the columns of the matrix span the space orthogonal to and is again a unitary matrix with columns spanning the interference subspace which is assumed to be of dimension . is a directional weighting matrix, , denotes the set of directions of interest, and is a directional weighting function. If we use no directional weighting, , the CAPS weight vector simplifies to where denotes the projection onto the space spanned by the columns of and . 4.3. Determination of the Dimension of Jammer Subspace (dimJSS) Subspace methods require an estimate of the dimension of the interference subspace. Usually this is derived from the sample eigenvalues. For complicated scenarios and small sample size, a clear decision of what constitutes a dominant eigenvalue may be difficult. There are two principle approaches to determine the number of dominant eigenvalues, information theoretic criteria and noise power tests. The information theoretic criteria are often based on the sphericity test criterion; see, for example, , where denote the eigenvalues of the estimated covariance matrix ordered in decreasing magnitude. The ratio of the arithmetic to geometric mean of the eigenvalues is a measure of the equality of the eigenvalues. The information theoretic criteria minimize this ratio with a penalty function added; for example, the Akaike Information Criterion (AIC) and Minimum Description Length (MDL) choose dimJSS as the minimum of the following functions: The noise power threshold tests (WNT) assume that the noise power is known and just check the estimated noise power against this value, . This leads to the statistic and the decision is found if the test statistic is for the first time below the threshold: The symbol denotes the -percentage point of the -distribution with degrees of freedom. The probability to overestimate dimJSS is then asymptotically bounded by . More modern versions of this test have been derived, for example, . For small sample size, AIC and MDL are known for grossly overestimating the number of sources. In addition, bandwidth and array channels errors lead to a leakage of the dominant eigenvalues into the small eigenvalues, . Improved eigenvalue estimates for small sample size can mitigate this effect. The simplest way could be to use the asymptotic approximation using the well-known linkage factors, , More refined methods are also possible; see . However, as explained in , simple diagonal loading can improve AIC and MDL for small sample size and make these criteria robust against errors. For the WNT this loading is contained in the setting of the assumed noise level . Figure 8 shows an example of a comparison of MDL and AIC without any corrections, MDL and WNT with asymptotic correction (25), and MDL and WNT with diagonal loading of . The threshold for WNT was set for a probability to overestimate the target number of = 10%. The scenario consists of four sources at = −0.7, −0.55, −0.31, −0.24 with SNR of 18, 6, 20, 20.4 dB and a uniform linear antenna with 14 elements and 10% relative bandwidth leading to some eigenvalue leakage. Empirical probabilities were determined from 100 Monte Carlo trials. Note that the asymptotic correction seems to work better for WNT than for MDL. With diagonal loading, all decisions with both MDL and WNT were correct (equal to 4). A more thorough study of the small sample size dimJSS estimation problem considering the “effective number of identifiable signals” has been performed in , and a new modified information theoretic criterion has been derived. 5. Parameter Estimation and Superresolution The objective of radar processing is not to maximize the SNR but to detect targets and determine their parameters. For detection, the SNR is a sufficient statistic (for the likelihood ratio test); that is, if we maximize the SNR we maximize also the probability of detection. Only for these detected targets we have then a subsequent procedure to estimate the target parameters: direction, range, and possibly Doppler. Standard radar processing can be traced back to maximum likelihood estimation of a single target which leads to the matched filter, . The properties of the matched filter can be judged by the beam shape (for angle estimation) and by the ambiguity function (for range and Doppler estimation). If the ambiguity function has a narrow beam and sufficiently low sidelobes, the model of a single target is a good approximation as other targets are attenuated by the sidelobes. However, if we have closely spaced targets or high sidelobes, multiple target models have to be used for parameter estimation. A variety of such estimation methods have been introduced which we term here “superresolution methods.” Historically, these methods have often been introduced to improve the limited resolution of the matched filter. The resolution limit for classical beamforming is the 3 dB beamwidth. An antenna array provides spatial samples of the impinging wavefronts, and one may define a multitarget model for this case. This opens the possibility for enhanced resolution. These methods have been discussed since decades, and textbooks on this topic are available, for example, . We formulate here the angle parameter estimation problem (spatial domain), but corresponding versions can be applied in the time domain as well. In the spatial domain, we are faced with the typical problems of irregular sampling and subarray processing. From the many proposed methods, we mention here only some classical methods to show the connections and relationships. We have spectral methods which generate a spiky estimate of the angular spectral density like. Capon’s method: and MUSIC method (Multiple Signal Classification): with , and spanning the dominant subspace. An LMI-version instead of MUSIC would also be possible. The target directions are then found by the highest maxima of these spectra ( 1- or 2-dimensional maximizations). An alternative group of methods are parametric methods, which deliver only a set of “optimal” parameter estimates which explain in a sense the data for the inserted model by or dimensional optimization . Deterministic ML method (complex amplitudes are assumed deterministic): Stochastic ML method (complex amplitudes are complex Gaussian): where denotes the completely parameterized covariance matrix. A formulation with the unknown directions as the only parameters can be given as The deterministic ML method has some intuitive interpretations: (1), which means that the mean squared residual error after signal extraction is minimized.(2), which can be interpreted as maximizing a set of decoupled sum beams .(3) with , where we have partitioned the matrix of steering vectors into . This property is valid due to the projection decomposition lemma which says that for any partitioning we can write . If we keep the directions in fixed, this relation says that we have to maximize the scan pattern over while the sources in the directions of are deterministically nulled (see (7)). One can now perform the multidimensional maximization by alternating 1-dimensional maximizations and keeping the remaining directions fixed. This is the basis of the alternating projection (AP) method or IMP (Incremental MultiParameter) method, [22, page 105]. A typical feature of the MUSIC method is illustrated in Figure 9. This figure shows the excellent resolution in simulation while for real data the pattern looks almost the same as with Capon’s method. (a) Simulated data (b) Measured real data A result with real data with the deterministic ML method is shown in Figure 10. Minimization was performed here with a stochastic approximation method. This example shows in particular that the deterministic ML-method is able to resolve highly correlated targets which arise due to the reflection on the sea surface for low angle tracking. The behavior of the monopulse estimates reflect the variation of the phase differences of direct and reflected path between 0° and 180°. For 0° phase difference the monopulse points into the centre, for 180° it points outside the 2-target configuration. The problems of superresolution methods are described in [21, 23]. A main problem is the numerical effort of finding the maxima (one -dimensional optimization or 1-dimensional optimizations for a linear antenna). To mitigate this problem a stochastic approximation algorithm or the IMP method has been proposed for the deterministic ML method. The IMP method is an iteration of maximizations of an adaptively formed beam pattern. Therefore, the generalized monopulse method can be used for this purpose, see Section 7.1 and . Another problem is the exact knowledge of the signal model for all possible directions (the vector function ). The codomain of this function is sometimes called the array manifold. This is mainly a problem of antenna accuracy or calibration. While the transmission of a plane wave in the main beam direction can be quite accurately modeled (using calibration) this can be difficult in the sidelobe region. For an array with digital subarrays, superresolution has to be performed only with these subarray outputs. The array manifold has then to be taken at the subarray outputs as in (2). This manifold (the subarray patterns) is well modeled in the main beam region but often too imprecise in the sidelobe region to obtain a resolution better than the conventional. In that case it is advantageous to use a simplified array manifold model based only on the subarray gains and centers, called the Direct Uniform Manifold model (DUM). This simplified model has been successfully applied to MUSIC (called Spotlight MUSIC, ) and to the deterministic ML method. Using the DUM model requires little calibration effort and gives improved performance, . More refined parametric methods with higher asymptotic resolution property have been suggested (e.g., COMET, Covariance Matching Estimation Technique, ). However, application of such methods to real data often revealed no improvement (as is the case with MUSIC in Figure 9). The reason is that these methods are much more sensitive to the signal model than the accuracy of the system provides. A sensitivity with an very sharp ideal minimum of the objective function may lead to a measured data objective function where the minimum has completely disappeared. 5.2. Target Number Determination Superresolution is a combined target number and target parameter estimation problem. As a starting point all the methods of Section 4.3 can be used. If we use the detML method we can exploit that the objective function can be interpreted as the residual error between model (interpretation 2) and data. The WNT test statistic (23) is just an estimate of this quantity. The detML residual can therefore be used for this test instead of the sum of the eigenvalues. These methods may lead to a possibly overestimated target number. To determine the power allocated to each target a refined ML power estimate using the estimated directions can be used with as in (30). This estimate can even reveal correlations between the targets. This has been successfully demonstrated with the low angle tracking data of Figure 10. In case that some target power is too low, the target number can be reduced and the angle estimates can be updated. This is an iterative procedure of target number estimation and confirmation or reduction. This way, all target modeling can be accurately matched to the data. The deterministic ML method (28) together with the white noise test (24) is particularly suited for this kind of iterative model fitting. It has been implemented in an experimental system with a 7-element planar array at Fraunhofer FHR and was first reported in [21, page 81]. An example of the resulting output plot is shown in Figure 11. The estimated directions in the , -plane are shown by small dishes having a color according to the estimated target SNR corresponding to the color bar. The circle indicates the 3 dB contour of the sum beam. One can see that the two targets are at about 0.5 beamwidth separation. The directions were estimated by the stochastic approximation algorithm used in Figure 10. The test statistic for increasing the target number is shown by the right most bar. The thresholds for increasing the number are indicated by lines. The dashed line is the actually valid threshold (shown is the threshold for 2 targets). The target number can be reduced if the power falls below a threshold shown in two yellow bars in the middle. The whole estimation and testing procedure can also be performed adaptively with changing target situations. We applied it to two blinking targets alternating between the states “target 1 on”, “both targets on”, “target 2 on”, “both targets on”, and so forth. Clearly, these test works only if the estimation procedure has converged. This is indicated by the traffic light in the right up corner. We used a fixed empirically determined iteration number to switch the test procedure on (=green traffic light). All thresholds and iteration numbers have to be selected carefully. Otherwise, situations may arise where this adaptive procedure switches between two target models, for example, between 2 and 3 targets. The problem of resolution of two closely spaced targets becomes a particular problem in the so called threshold region, which denotes configurations where the SNR or the separation of the targets lead to an angular variance departing significantly from the Cramer-Rao bound (CRB). The design of the tests and this threshold region must be compatible to give consistent joint estimation-detection resolution result. These problems have been studied in [27, 28]. One way to achieve consistency and improving resolution proposed in is to detect and remove outliers in the data, which are basically responsible for the threshold effect. A general discussion about the achievable resolution and the best realistic representation of a target cluster can be found in . 6. Extension to Space-Time Arrays As mentioned in Section 2.4, there is mathematically no difference between spatial and temporal samples as long as the distributional assumptions are the same. The adaptive methods and superresolution methods presented in the previous sections can therefore be applied analogously in the time or space-time domain. In particular, subarraying in time domain is an important tool to reduce the numerical complexity for space-time adaptive processing (STAP) which is the general approach for adaptive clutter suppression for airborne radar, . With the formalism of transforming space-time 2D-beamforming of a data matrix into a usual beamforming operation of vectors introduced in (4), the presented adaptive beamforming and superresolution methods can be easily transformed into corresponding subarrayed space-time methods. Figure 12 shows an example of an efficient space-time subarraying scheme used for STAP clutter cancellation for airborne radar. 7. Embedding of Array Processing into Full Radar Data Processing A key problem that has to be recognized is that the task of a radar is not to maximize the SNR, but to give the best relevant information about the targets after all processing. This means that for implementing refined methods of interference suppression or superresolution we have also to consider the effect on the subsequent processing. To get optimum performance all subsequent processing should exploit the properties of the refined array signal processing methods applied before. In particular it has been shown that for the tasks of detection, angle estimation and tracking significant improvements can be achieved by considering special features. 7.1. Adaptive Monopulse Monopulse is an established technique for rapid and precise angle estimation with array antennas. It is based on two beams formed in parallel, a sum beam and a difference beam. The difference beam is zero at the position of the maximum of the sum beam. The ratio of both beams gives an error value that indicates the offset of a target from the sum beam pointing direction. In fact, it can be shown that this monopulse estimator is an approximation of the Maximum-Likelihood angle estimator, . The monopulse estimator has been generalized in to arrays with arbitrary subarrays and arbitrary sum and difference beams. When adaptive beams are used the shape of the sum beam will be distorted due to the interference that is to be suppressed. The difference beam must adaptively suppress the interference as well, which leads to another distortion. Then the ratio of both beams will no more indicate the target direction. The generalized monopulse procedure of provides correction values to compensate these distortions. The generalized monopulse formula for estimating angles with a planar array and sum and difference beams formed into direction is where is a slope correction matrix and is a bias correction. is the monopulse ratio formed with the measured difference and sum beam outputs and , respectively, with difference and sum beam weight vectors , (analogous for elevation estimation with ). The monopulse ratio is a function of the unknown target directions . Let the vector of monopulse ratios be denoted by . The correction quantities are determined such that the expectation of the error is unbiased and a linear function with slope 1 is approximated. More precisely, for the following function of the unknown target direction: we require These conditions can only approximately be fulfilled for sufficiently high SNR. Then, one obtains for the bias correction for a pointing direction , For the elements of the inverse slope correction matrix , one obtains with or and or , and denotes the derivative . In general, these are fixed antenna determined quantities. For example, for omnidirectional antenna elements, and phase steering at the elements we have , where is the antenna element gain, and . It is important to note that this formula is independent of any scaling of the difference and sum weights. Constant factors in the difference and sum weight will be cancelled by the corresponding slope correction. Figure 13 shows theoretically calculated bias and variances for this corrected generalized monopulse using the formulas of for the array of Figure 2. The biases are shown by arrows for different possible single target positions with the standard deviation ellipses at the tip. A jammer is located in the asterisk symbol direction with JNR = 27 dB. The hypothetical target has a SNR of 6 dB. The 3 dB contour of the unadapted sum beam is shown by a dashed circle. The 3 dB contour of the adapted beam will be of course different. One can see that in the beam pointing direction the bias is zero and the variance is small. The errors increase for target directions on the skirt of the main beam and close to the jammer. The large bias may not be satisfying. However, one may repeat the monopulse procedure by repeating the monopulse estimate with a look direction steered at subarray level into the new estimated direction. This is an all-offline procedure with the given subarray data. No new transmit pulse is needed. We have called this the multistep monopulse procedure . Multistep monopulse reduces the bias considerably with only one additional iteration as shown in Figure 14. The variances appearing in Figure 13 are virtually not changed with the multistep monopulse procedure and are omitted for better visibility. 7.2. Adaptive Detection For detection with adaptive beams, the normal test procedure is not adequate because we have a test statistic depending on two different kinds of random data: the training data for the adaptive weight and the data under test. Various kinds of tests have been developed accounting for this fact. The first and basic test statistics were the GLRT, , the AMF detector, , and the ACE detector, . These have the form The quantities , , are here all generated at the subarray outputs, denotes the plane wave model for a direction . Basic properties of these tests are The AMF detector represents an estimate of the signal-to-noise ratio because it can be written as This provides a meaningful physical interpretation. A complete statistical description of these tests has been given in very compact form in [32, 33]. These results are valid as well for planar arrays with irregular subarrays and also mismatched weighting vector. Actually, all these detectors use the adaptive weight of the SMI algorithm which has unsatisfactory performance as mentioned in Section 4.2. The unsatisfactory finite sample performance is just the motivation for introducing weight estimators like LSMI, LMI, or CAPS. Clutter, insufficient adaptive suppression and surprise interference are the motivation for requiring low sidelobes. Recently several more complicated adaptive detectors have been introduced with the aim of achieving additional robustness properties, [34–38]. However, another and quite simple way would be to generalize the tests of (36), (37), (38) to arbitrary weight vectors with the aim of inserting well known robust weights as derived in Section 4.1. This has been done in . First, we observe that the formulation of (40) can be used for any weight vector. Second, one can observe that the ACE and GLRT have the form of a sidelobe blanking device. In particular it has already been shown in that diagonal loading provides significant better detection performance. A guard channel is implemented in radar systems to eliminate impulsive interference (hostile or from other neighboring radars) using the sidelobe blanking (SLB) device. The guard channel receives data from an omnidirectional antenna element which is amplified such that its power level is above the sidelobe level of the highly directional radar antenna, but below the power of the radar main beam, [1, page 9.9]. If the received signal power in the guard channel is above the power of the main channel, this must be a signal coming via the sidelobes. Such signals will be blanked. If the guard channel power is below the main channel power it is considered as a detection. With phased arrays it is not necessary to provide an external omnidirectional guard channel. Such a channel can be generated from the antenna itself; all the required information is in the antenna. We may use the noncoherent sum of the subarrays as guard channel. This is the same as the average omnidirectional power. Some shaping of the guard pattern can be achieved by using a weighting for the noncoherent sum: If all subarrays are equal, a uniform weighting may be suitable; for unequal irregular subarrays as in Figure 2 the different contributions of the subarrays can be weighted. The directivity pattern of such guard channel is given by . More generally, we may use a combination of noncoherent and coherent sums of the subarrays with weights contained in the matrices , , respectively, Examples of such kind of guard channels are shown in Figure 15 for the generic array of Figure 2 with −35 dB Taylor weighing for low sidelobes. The nice feature of these guard channels is (i) that they automatically scan together with the antenna look direction, and (ii) that they can easily be made adaptive. This is required if we want to use the SLB device in the presence of CW plus impulsive interference. A CW jammer would make the SLB blank all range cells, that is, would just switch off the radar. To generate an adaptive guard channel we only have to replace in (42) the data vector of the cell under test (CUT) by the pre-whitened data . Then, the test statistic can be written as , where for ACE and for GLRT. Hence is just the incoherent sum of the pre-whitened subarray outputs; in other words, can be interpreted as an AMF detector with an adaptive guard channel and the same with guard channel on a pedestal. Figure 16 shows examples of some adapted guard channels generated with the generic array of Figure 2 and −35 dB Taylor weighting. The unadapted patterns are shown by dashed lines. (a) Uniform subarray weighting (b) Power equalized weighting (c) Power equalized + difference weighting (a) Weighting for equal subarray power (b) Difference type guard with weighting for equal subarray power This is the adaptive generalization of the usual sidelobe blanking device (SLB) and the AMF, ACE and GLRT tests can be used as extension of the SLB detector to the adaptive case, , called the 2D adaptive sidelobe blanking (ASB) detector. The AMF is then the test for the presence of a potential target and the generalized ACE or GRLT are used confirming this target or adaptive sidelobe blanking. A problem with these modified tests is to define a suitable threshold for detection. For arbitrary weight vector it is nearly impossible to determine this analytically. In the detection margin has been introduced as an empirical tool for judging a good balance between the AMF and ASB threshold for given jammer scenarios. The detection margin is defined as the difference between the expectation of the AMF statistic and the guard channel, where the expectation is taken only over the interference complex amplitudes for a known interference scenario. In addition one can also calculate the standard deviation of these patterns. The performance against jammers close to the main lobe is the critical feature. The detection margin provides the mean levels together with standard deviations of the patterns. An example of the detection margin is shown in Figure 17 (same antenna and weighting as in Figures 15 and 16). Comparing the variances of the ACE and GLRT guard channels in revealed that the GLRT guard performs significantly better in terms of fluctuations. The GLRT guard channel may therefore be preferred for its better sidelobe performance and higher statistical stability. 7.3. Adaptive Tracking A key feature of ABF is that overall performance is dramatically influenced by the proximity of the main beam to an interference source. The task of target tracking in the proximity of a jammer is of high operational relevance. In fact, the information on the jammer direction can be made available by a jammer mapping mode, which determines the direction of the interferences by a background procedure using already available data. Jammers are typically strong emitters and thus easy to detect. In particular, the Spotlight MUSIC method working with subarray outputs is suited for jammer mapping with a multifunction radar. Let us assume here for simplicity that the jammer direction is known. This is highly important information for the tracking algorithm of a multifunction radar where the tracker determines the pointing direction of the beam. We will use for angle estimation the adaptive monopulse procedure of Section 7.1. ABF will form beams with a notch in the jammer direction. Therefore one cannot expect target echoes from directions close to the jammer and therefore it does not make sense to steer the beam into the jammer notch. Furthermore, in the case of a missing measurement of a tracked target inside the jammer notch, the lack of a successful detection supports the conclusion that this negative contact is a direct result of jammer nulling by ABF. This is so-called negative information . In this situation we can use the direction of the jammer as a pseudomeasurement to update and maintain the track file. The width of the jammer notch defines the uncertainty of this pseudo measurement. Moreover, if one knows the jammer direction one can use the theoretically calculated variances for the adaptive monopulse estimate of as a priori information in the tracking filter. The adaptive monopulse can have very eccentric uncertainty ellipses as shown in Figure 13 which is highly relevant for the tracker. The large bias appearing in Figure 13, which is not known by the tracker, can be reduced by applying the multistep monopulse procedure, . All these techniques have been implemented in a tracking algorithm and refined by a number of stabilization measures in . The following special measures for ABF tracking have been implemented and are graphically visualized in Figure 18.(i)Look direction stabilization: the monopulse estimate may deliver measurements outside of the 3 dB contour of the sum beam. Such estimates are also heavily biased, especially for look directions close to the jammer, despite the use of the multistep monopulse procedure. Estimates of that kind are therefore corrected by projecting them onto the boundary circle of sum beam contour.(ii)Detection threshold: only those measurements are considered in the update step of the tracking algorithm whose sum beam power is above a certain detection threshold (typically 13 dB). This guarantees useful and valuable monopulse estimates. It is well known that the variance of the monopulse estimate decreases monotonically with this threshold increasing. (iii)Adjustment of antenna look direction: look directions in the jammer notch should generally be avoided due to the expected lack of good measurements. In case that the proposed look direction lies in the jammer notch, we select an adjusted direction on the skirt of the jammer notch.(iv)Variable measurement covariance: a variable covariance matrix of the adaptive monopulse estimation according to is considered only for a mainlobe jammer situation. For jammers in the sidelobes, there is little effect on the angle estimates, and we can use the fixed covariance matrix of the nonjammed case. (v)QuadSearch and Pseudomeasurements: if the predicted target direction lies inside the jammer notch and if, despite all adjustments of the antenna look direction, the target is not detected, a specific search pattern is initiated (named QuadSearch) which uses look directions on the skirt of the jammer notch to obtain acceptable monopulse estimates. If this procedure does not lead to a detection, we know that the target is hidden in the jammer notch and we cannot see it. We use then the direction of the jammer as a pseudobearing measurement to maintain the track file. The pseudomeasurement noise is determined by the width of the jammer notch.(vi)LocSearch: in case of a permanent lack of detections (e.g., for three consecutive scans) while the track position lies outside the jammer notch, a specific search pattern is initiated (named LocSearch) that is similar to the QuadSearch. The new look directions lie on the circle of certain radius around the predicted target direction.(vii)Modeling of target dynamics: the selection of a suitable dynamics model plays a major role for the quality of tracking results. In this context, the so-called interacting multiple model (IMM) is a well-known method to reliably track even those objects whose dynamic behavior remains constant only during certain periods.(viii)Gating: in the vicinity of the jammer, the predicted target direction (as an approximation of the true value) is used to compute the variable angle measurement covariance. Strictly speaking, this is only valid exactly in the particular look direction. Moreover, the tracking algorithm regards all incoming sensor data as unbiased measurements. To avoid track instabilities, an acceptance region is defined for each measurement depending on the predicted target state and the assumed measurement accuracy. Sensor reports lying outside this gate are considered as invalid. In order to evaluate our stabilization measures we considered a realistic air-to-air target tracking scenario . Figure 19 provides an overview of the different platform trajectories. In this scenario, the sensor (on a forward looking radar platform flying with a constant speed of 265 m/s) employs the antenna array of Figure 2 (sum beamwidth BW = 3.4°, field of view 120°, scan interval 1 s) and approaches the target (at velocity 300 m/s), which thereupon veers away after a short time. During this time, the target is hidden twice in the jammer notch of the standoff jammer (SOJ)—first for 3 s and then again for 4 s. The SOJ is on patrol (at 235 m/s) and follows a predefined race track at constant altitude. Figure 20 shows exemplary the evaluation of the azimuth measurements and estimates over time in a window where the target first passes through the jammer notch. The different error bars of a single measurement illustrate the approximation error of the variable measurement covariance: denotes the true azimuth standard deviation (std) which is generated in the antenna simulation; corresponds to the std which is used in the tracking algorithm. More precisely, the tracking program computes the adaptive angle measurement covariance only in the vicinity of the jammer with a diameter of this zone of 8.5°. Outside of this region, the tracking algorithm uses a constant std of 0.004 for both components of the angle measurement. The constant std for the other parameters are 75 m and 7.5 m/s for range and range-rate measurements. The signal-to-noise and jammer-to-noise ratios were set to 26 dB and 27 dB at a reference range of 70 km. From Figure 20 the benefits of using pseudobearing measurements become apparent. From these investigations, it turned out that tracking only with adaptive beamforming and adaptive monopulse nearly always leads to track loss in the vicinity of the jammer. With additional stabilization measures that did not require the knowledge of the jammer direction (projection of monopulse estimate, detection threshold, LocSearch, gating) still track instabilities occurred culminating finally in track loss. An advanced tracking version which used pseudomeasurements mitigated this problem to some degree. Finally, the additional consideration of the variable measurement covariance with a better estimate of the highly variable shape of the angle uncertainty ellipse resulted in significantly fewer measurements that were excluded due to gating. In this case all the stabilization measures could not only improve track continuity, but also track accuracy and thus track stability, . This tells us that it is absolutely necessary to use all information of the adaptive process for the tracker to achieve the goal of detection and tracking in the vicinity of the interference. 8. Conclusions and Final Remarks In this paper, we have pointed out the links between array signal processing and antenna design, hardware constraints and target detection, and parameter estimation and tracking. More specifically, we have discussed the following features.(i)Interference suppression by deterministic and adaptive pattern shaping: both approaches can be reasonably combined. Applying ABF after deterministic sidelobe reduction allows reducing the requirements on the low sidelobe level. Special techniques are available to make ABF preserve the low sidelobe level.(ii)General principles and relationships between ABF algorithms and superresolution methods have been discussed, like dependency on the sample number, robustness, the benefits of subspace methods, problems of determining the signal/interference subspace, and interference suppression/resolution limit. (iii)Array signal processing methods like adaptive beamforming and superresolution methods can be applied to subarrays generated from a large fully filled array. This means applying these methods to the sparse superarray formed by the subarray centers. We have pointed out problems and solutions for this special array problem.(iv)ABF can be combined with superresolution in a canonical way by applying the pre-whiten and match principle to the data and the signal model vector. (v)All array signal processing methods can be extended to space-time processing (arrays) by defining a corresponding space-time plane wave model. (vi)Superresolution is a joint detection-estimation problem. One has to determine a multitarget model which contains the number, directions and powers of the targets. These parameters are strongly coupled. A practical joint estimation and detection procedure has been presented.(vii)The problems for implementation in real system have been discussed, in particular the effects of limited knowledge of the array manifold, effect of channel errors, eigenvalue leakage, unequal noise power in array channels, and dynamic range of AD-converters.(viii)For achieving best performance an adaptation of the processing subsequent to ABF is necessary. Direction estimation can be accommodated by using ABF-monopulse; the detector can be accommodated by adaptive detection with ASLB, and the tracking algorithms can be extended to adaptive tracking and track management with jammer mapping. With a single array signal processing method alone no significant improvement will be obtained. The methods have to be reasonably embedded in the whole system, and all functionalities have to be mutually tuned and balanced. This is a task for future research. The presented approaches constitute only a first ad hoc step, and more thorough studies are required. Note that in most cases tuning the functionalities is mainly a software problem. So, there is the possibility to upgrade existing systems softly and step-wise. The main part of this work was performed while the author was with the Fraunhofer Institute for High Frequency Physics and Radar Techniques (FHR) in Wachtberg, Germany. M. I. Skolnik, Radar Handbook, McGraw Hill, 2nd edition, 1990. M. A. Richards, J. A. Scheer, and W. A. Holden, Principles of Modern Radar, SciTech Publishing, 2010. W. D. Wirth, Radar Techniques Using Array Antennas, IEE Publishers, 2001. R. Klemm, Principles of Space-Time Adaptive Processing, IET Publishers, London, UK, 3rd edition, 2006. U. Nickel, “Subarray configurations for digital beamforming with low sidelobes and adaptive interference suppression,” in Proceedings of the IEEE International Radar Conference, pp. 714–719, Alexandria, Egypt, May 1995.View at: Google Scholar U. Nickel, “Properties of digital beamforming with subarrays,” in Proceedings of the International Conference on Radar (CIE '06), pp. 6–19, Shanghai, China, October 2006.View at: Google Scholar W. Bürger, “Sidelobe forming for ground clutter and jammer suppression for airborne active array radar,” in Proceedings of the IEEE International Symposium on Phased Array Systems and Technology, Boston, Mass, USA, 2003.View at: Google Scholar Y. Hua, A. B. Gershman, and Q. Cheng, High Resolution and Robust Signal Processing, Marcel Dekker, 2004. U. Nickel, “Adaptive Beamforming for Phased Array Radars,” in Proceedings of the IEEE International Radar Symposium (IRS '98), pp. 897–906, DGON and VDE/ITG, September 1998.View at: Google Scholar C. H. Gierull, “Fast and effective method for low-rank interference suppression in presence of channel errors,” Electronics Letters, vol. 34, no. 6, pp. 518–520, 1998.View at: Google Scholar G. M. Herbert, “New projection based algorithm for low sidelobe pattern synthesis in adaptive arrays,” in Proceedings of the Radar Edinburgh International Conference, pp. 396–400, October 1997.View at: Google Scholar U. Nickel, “Determination of the dimension of the signal subspace for small sample size,” in Proceedings of the IASTED international conference on Signal Processing and Communication Systems, pp. 119–122, IASTED/Acta Press, 1998.View at: Google Scholar U. Nickel, “On the influence of channel errors on array signal processing methods,” International Journal of Electronics and Communications, vol. 47, no. 4, pp. 209–219, 1993.View at: Google Scholar R. J. Muirhead, Aspects of Multivariate Analysis Theory, John Wiley & Sons, New York, NY, USA, 1982. U. Nickel, “Radar target parameter estimation with antenna arrays,” in Radar Array Processing, S. Haykin, J. Litva, and T. J. Shepherd, Eds., pp. 47–98, Springer, 1993.View at: Google Scholar S. Haykin, Advances in Spectrum Analysis and Array Processing. Vol. II, Prentice Hall, 1991. U. Nickel, “Aspects of implementing super-resolution methods into phased array radar,” International Journal of Electronics and Communications, vol. 53, no. 6, pp. 315–323, 1999.View at: Google Scholar B. Ottersten, P. Stoica, and R. Roy, “Covariance matching estimation techniques for array signal processing applications,” Digital Signal Processing, vol. 8, no. 3, pp. 185–210, 1998.View at: Google Scholar Y. I. Abramovich and B. A. Johnson, “Detection-estimation of very close emitters: performance breakdown, ambiguity, and general statistical analysis of maximum-likelihood estimation,” IEEE Transactions on Signal Processing, vol. 58, no. 7, pp. 3647–3660, 2010.View at: Publisher Site | Google Scholar E. J. Kelly, “Performance of an adaptive detection algorithm; rejection of unwanted signals,” IEEE Transactions on Aerospace and Electronic Systems, vol. 25, no. 2, pp. 122–133, 1992.View at: Google Scholar M. Feldmann and U. Nickel, “Target parameter estimation and tracking with adaptive beamforming,” in Proceedings of the International Radar Symposium (IRS '11), pp. 585–590, Leipzig, Germany, September 2011.View at: Google Scholar

s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335365.63/warc/CC-MAIN-20220929194230-20220929224230-00305.warc.gz

CC-MAIN-2022-40

http://www.oocities.org/tokyo/garden/5301/1.html

math

CONJECTURE is a conclusion based on examples. COUNTEREXAMPLE is an example that shows a conjecture is to be false. Example of Conjectures for a rectangle a) If a quadrilateral has four equal angles, it has four equal sides. b) The length of a rectangle is always double its width c) The opposite sides of a parallelogram are equal in length. Out of the three conjectures given, a) and b) are the counterexamples. Examples of false conjecture with their true counterexamples A number that is not positive is negative. If 1 is added to an off number, the result is always an even number The altitude of a triangle always lies inside the triangle An altitude of an obtuse triangle lies outside it. Every rectangle is a square Any rectangle in which its length is not equal to its width is not a square.

s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259126.83/warc/CC-MAIN-20190526105248-20190526131248-00447.warc.gz

CC-MAIN-2019-22

http://imechanica.org/node/15150

math

You are here Ellipsoidal Domain with Piecewise Nonuniform Eigenstrain Field in One of Joined Isotropic Half-Spaces [img_assist|nid=15151|title=Ellipsoidal inclusion and its mirror image in two joined semi-infinite solids|desc=|link=none|align=left|width=267|height=326]Abstract Consider an arbitrarily oriented ellipsoidal domain near the interface of an isotropic bimaterial space. It is assumed that a general class of piecewise nonuniform dilatational eigenstrain field is distributed within the ellipsoidal domain. We state and prove two theorems relevant to prediction of the nature of the induced displacement field for the interior and exterior points of the ellipsoidal domain. As a resultant the exact analytical expression of the elastic fields are obtained rigorously. In this work, we introduce a new Eshelby-like tensor, denoted by A. In particular, the closed-form expressions for A associated with the interior points of spherical and cylindrical inclusion are derived. The stress field is presented for a single ellipsoidal inclusion which undergoes a Gaussian distribution of eigenstrain field and one of the principal axes of the domain is perpendicular to the interface. For the limiting case of spherical inclusion the closed-form solution is obtained and the associated strain energy is discussed. For further demonstration, we provide two examples of two concentric spheres and three concentric cylinders with eigenstrain field distributions which are descriptive of the general class of functions defined in this paper. The effect of some parameters such as distance between the inclusion and the interface, and the ratio of the shear moduli of the two media on the induced elastic fields are examined.

s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123632.58/warc/CC-MAIN-20170423031203-00479-ip-10-145-167-34.ec2.internal.warc.gz

CC-MAIN-2017-17

https://www.manhattanreefs.com/forum/chemistry/144208-how-dosing-help.html

math

Check the calculator I posted in the Calculator stickie.There may not be a good answer to this question post setup of a tank but how does one figure out displacement? I've been trying to figure out my total water volume as I've been gearing up to dose BRS 2-part. I have a 90 gallon with a 30 gal sump and lots of rock but I have no idea how to figure out its displacement. I've heard people mention weight of rock but what would that have to do with it? If I place a sealed "orb" or something that weighs next to nothing in a tank along side a rock of equal mass they're displacing equally aren't they?

s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540499389.15/warc/CC-MAIN-20191207105754-20191207133754-00167.warc.gz

CC-MAIN-2019-51

https://www.justanswer.co.uk/volkswagen/9zdg0-glow-plug-light-stays-2sec-engine-starts-ok.html

math

Ask a Volkswagen Question, Get an Answer ASAP! I'd check that you're getting full power to the glow-plugs, they pull a lot of current so take care when checking but see if the relay is clicking when the ignition is turned on first and also check the fuse if this is OK check to see if the engine earth strap is also OK.If the plugs haven't been changed in the last 20K then they may have to be replaced. You can test the glow-plugs with a multimeter by measuring the resistance across the plug ( between the power connection and the body) it should be around 4-8ohms if its tending to infinity / open circuit the plug is faulty or by using a clip on current clamp, either on the supply wire to glow plugs or onto engine earth, with glow plug light on you should see 15-20amps for each glow plug fitted, 4 cylinders would be approximately 60-80amps. do you still need help? Bear in mind that the site takes a deposit from you at the beginning and this is held by the site until you rate my answer at which point the cash is split between the site and the expert. I am only paid for my work on this question if you rate my answer, using the star system at the top of the screen. Please do not forget! Thank you It should be###-##-#### OK thats a pattern part but its the correct spec so lets assume its OK In which case I'd move onto checking the resistance of all of the glow plugs as the next step it’s also worth considering fitting a new fuel filter as if only slightly blocked this can lower fuel supply pressure and choke the main pump, the pump will be more sensitive to this when its cold as diesel thickens considerably with low temperatures.

s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257649931.17/warc/CC-MAIN-20180324054204-20180324074204-00024.warc.gz

CC-MAIN-2018-13

http://www.wyzant.com/Chantilly_GMAT_tutors.aspx

math

"William and Mary Math Tutor For Calculus II and Below, SAT, ACT prep" ...g., Acing the SAT I Math, 2nd Edition by Greenhall Publishing is probably the best SAT Math prep book on the market). I also tutor the GRE (Graduate Record Examination) and GMAT (Graduate Management Admission Test), which are significantly harder standardized tests for graduate school. I tutor the GRE and GMAT at a much higher rate than I charge... 10+ subjects, including GMAT

s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696400149/warc/CC-MAIN-20130516092640-00083-ip-10-60-113-184.ec2.internal.warc.gz

CC-MAIN-2013-20

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=135&t=42537

math

5 posts • Page 1 of 1 Both can give you the same thing, you just need to look at what you're given and determine which formula has it ex. if you're given delta H, T, and delta S, then you'll want to use delta G = delta H - T delta S It is also important to note that you might get slightly different answers when using the two different methods due to rounding differences since you are using a table of information for one and information given in the problem for the other. Don’t forget that there is also this equation: ∆G = ∆G° + RTlnQ A lot of homework questions about Gibbs free energy can only be answered with this. It’s generally used when given a temperature value, a K value, and concentations/partial pressures of reactants and products to calculate Q. Who is online Users browsing this forum: No registered users and 1 guest

s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178374616.70/warc/CC-MAIN-20210306070129-20210306100129-00015.warc.gz

CC-MAIN-2021-10

https://cache.kzoo.edu/items/55bff065-eff4-4f70-8fd4-24f9f55d998e/full

math

Recognizing Simple Groups by Their Codegree Sets |Intermont, Michele, 1967- |An arithmetic property of a group G is a property that can be expressed solely in terms of numbers. The restrictions that certain arithmetic properties place on the structure of a group is a well-studied and fruitful area of research; two of the most well-known theorems pertaining to arithmetic properties assert that all groups of order 2 are abelian and that all finite groups of odd order are solvable. While both of these theorems arise from a single arithmetic property, namely the order of a group, strong conjectures have been made concerning sets of arithmetic properties. For example, in 2000, Huppert conjectured that if a finite nonabelian simple group H and a finite group G share the same character degree set, then G ∼= H × A for some abelian group A. More recently, a stronger conjecture, often called the codegree version of Huppert’s conjecture, has been posed as question 20.79 in the Kourovka Notebook: if H is a nonabelian simple group and G is a finite group such that H and G have equal codegree sets, then G ∼= H. In other words, nonabelian simple groups are recognizable by their codegree sets. Huppert’s codegree conjecture has been verified for several simple groups, but it has yet to be completely proved. In this paper, we verify this conjecture for the sporadic groups and the simple alternating groups. |Kalamazoo College Mathematics Senior Individualized Projects Collection |U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder. |Recognizing Simple Groups by Their Codegree Sets

s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817073.16/warc/CC-MAIN-20240416062523-20240416092523-00380.warc.gz

CC-MAIN-2024-18

http://www.bookstoread.com/main/popup-window-java.htm

math

Perimeter of Polygons The perimeter of a polygon is the sum of the lengths of its sides. It is one-dimensional and is measured in linear units. Think of perimeter as the length of the fence around a yard. A square and an equilateral triangle are examples of a regular polygon. Another way to find the perimeter of a regular polygon is to multiply the number of sides in the polygon by the length of one side.

s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084892059.90/warc/CC-MAIN-20180123171440-20180123191440-00644.warc.gz

CC-MAIN-2018-05

http://courses.bc.edu/course/MATH/4462

math

MATH 4462 Topology (Fall: 3 ) This course is an introduction to point-set topology. Topics include topological spaces, continuous functions, connectedness, compactness, metric spaces, the Urysohn Metrization Theorem, manifolds, the fundamental group, and the classification of surfaces. We will also discuss applications of these concepts to problems in science and engineering. Last Updated: 27-May-14

s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891811795.10/warc/CC-MAIN-20180218081112-20180218101112-00046.warc.gz

CC-MAIN-2018-09

https://www.caclubindia.com/forum/solve-170812.asp

math

500 is the principal for 12 years (i assumed that 13th year only intrest accrued and no princiapal was deposited) 39000 in the way that - for the first year no interest 2nd year - interest on500 @ 12 % 3 rd year- Intt on1000 @ 12% and so on Pardon me!! I took the interest @ 12%....

s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999210.22/warc/CC-MAIN-20190620105329-20190620131329-00443.warc.gz

CC-MAIN-2019-26

https://books.google.com.jm/books?id=uzc7AQAAIAAJ&pg=PA216&vq=base&dq=editions:UOM39015063895950&lr=&output=html_text&source=gbs_toc_r&cad=4

math

« PreviousContinue » By considering the arc AM, and its supplement AM', and recollecting what has been said, we readily see that, sin (an arc)=sin (its supplement) cos (an arc)=-cos (its supplement) It is no less evident, that if one or several circumferences were added to any arc AM, it would still terminate exactly at the point M, and the arc thus increased would have the same sine as the arc AM; hence if C represent a whole circumference or 360°, we shall have sin x=sin (C+x)=sin x=sin (2C+x), &c. The same observation is applicable to the cosine, tangent, &c. Hence it appears, that whatever be the magnitude of x the proposed arc, its sine may always be expressed, with a proper sign, by the sine of an arc less than 180°. For, in the first place, we may subtract 360° from the arc x as often as they are contained in it; and y being the remainder, we shall have sin x=sin y. Then if y is greater than 180°, make y=180° +z, and we have sin y=—sin z. Thus all the cases are reduced to that in which the proposed arc is less than 180°; and since we farther have sin (90°+x)=sin (90°-x), they are likewise ultimately reducible to the case, in which the proposed arc is between zero and 90°. XIV. The cosines are always reducible to sines, by means of the formula cos A=sin (90°-A); or if we require it, by means of the formula cos A=sin (90°+A): and thus, if we can find the value of the sines in all possible cases, we can also find that of the cosines. Besides, as has already been shown, that the negative cosines are separated from the positive cosines by the diameter DE; all the arcs whose extremities fall on the right side of DE, having a positive cosine, while those whose extremities fall on the left have a negative cosine. Thus from 0° to 90° the cosines are positive; from 90° to 270° they are negative; from 270° to 360° they again become positive; and after a whole revolution they assume the same values as in the preceding revolution, for cos (360°+x)=cos x. From these explanations, it will evidently appear, that the sines and cosines of the various arcs which are multiples of the quadrant have the following values: sin 0°=0 sin 90°-R sin 180°=0 sin 270°-R sin 360°=0 sin 450°=R. sin 540°-0 sin 630°-R sin 720°=0 sin 810°-R cos 90° 0 COS 0° R And generally, k designating any whole number we shall sin 2k. 90° 0, cos (2k+1). 90°=0, cos 4k. 90°=R, sin (4k+1). 90°=R, sin (4k-1). 90° ——R, What we have just said concerning the sines and cosines renders it unnecessary for us to enter into any particular detail respecting the tangents, cotangents, &c. of arcs greater than 180°; the value of these quantities are always easily deduced from those of the sines and cosines of the same arcs: as we shall see by the formulas, which we now proceed to explain. THEOREMS AND FORMULAS RELATING TO SINES, COSINES, TANGENTS, &c. XV. The sine of an arc is half the chord which subtends a double arc. in other words, the sine of a third part of the right angle is equal to the half of the radius XVI. The square of the sine of an arc, together with the square of the cosine, is equal to the square of the radius; so that in general terms we have sin A+cos A=R2. This property results immediately from the right-angled triangle CMP, in which MP2+CP2-CM2. It follows that when the sine of an arc is given, its cosine may be found, and reciprocally, by means of the formulas cos A=√(R2-sin A), and sin A=±√(R2-cos2A). The sign of these formulas is +, or —, because the same sine MP answers to the two arcs AM, AM', whose cosines CP, CP', are equal and have contrary signs; and the same cosine CP answers to the two arcs AM, AN, whose signs MP, PN, are also equal, and have contrary signs. Thus, for example, having found sin 30°=1R, we may deduce from it cos 30°, or sin 60°= √(R2—R2)=√ R2=†Ř√3. XVII. The sine and cosine of an arc A being given, it is required to find the tangent, secant, cotangent, and cosecant of the The triangles CPM, CAT, CDS, being similar, we have the proportions: CP: PM :: CA: AT; or cos A: sin A:: R: tang A: CP: CM:: CA: CT; or cos A: R:: R: sec A= PM: CP:: CD: DS; or sin A: cos A:: R: cot A= PM: CM:: CD: CS; or sin A: R:: R: cosec A R sin A cos A R cos A which are the four formulas required. It may also be observed, that the two last formulas might be deduced from the first two, by simply putting 90°-A instead of A. From these formulas, may be deduced the values, with their proper signs, of the tangents, secants, &c. belonging to any arc whose sine and cosine are known; and since the progressive law of the sines and cosines, according to the different arcs to which they relate, has been developed already, it is unnecessary to say more of the law which regulates the tangents and secants. By means of these formulas, several results, which have already been obtained concerning the trigonometrical lines, may be confirmed. If, for example, we make A=90°, we shall have sin A=R, cos A=0; and consequently tang 90°= R2 an expression which designates an infinite quantity; for, the quotient of radius divided by a very small quantity, is very great, and increases as the divisor diminishes; hence, the quotient of the radius divided by zero is greater than any finite quantity, The tangent being equal to R.- S and cotangent to R. Cos it follows that tangent and cotangent will both be positive when the sine and cosine have like algebraic signs, and both negative, when the sine and cosine have contrary algebraic signs. Hence, the tangent and cotangent have the same sign in the diagonal quadrants: that is, positive in the 1st and 3d, and negative in the 2d and 4th; results agreeing with those of Art. XII. It is also apparent, from the above formulas, that the secant has always the same algebraic sign as the cosine, and the cosecant the same as the sine. Hence, the secant is positive on the right of the vertical diameter DE, and negative on the left of it; the cosecant is positive above the diameter BA, and negative below it: that is, the secant is positive in the 1st and 4th quadrants, and negative in the 2d and 3d: the cosecant is positive in the 1st and 2d, and negative in the 3d and 4th. XVIII. The formulas of the preceding Article, combined with each other and with the equation sin 2A+cos 2A=R2, furnish some others worthy of attention. First we have R2 + tang2 AR2 + R2 (sin2 A+ cos2 A). cos 2A R2 sin A hence R2+tang2 A÷sec2 A, a formula which might be immediately deduced from the rightangled triangle CAT. By these formulas, or by the right-angled triangle CDS, we have also R2+cot2 Acosec2 A. Lastly, by taking the product of the two formulas tang A= Resin A and cot A= R cos A formula which gives. cot A= we have tang Ax cot A=R2, a Hence cot A cot B: tang B: tang A; that is, the colangents of two arcs are reciprocally proportional to their tangents. The formula cot Ax tang A=R might be deduced immediately, by comparing the similar triangles CAT, CDS, which give AT CA: CD DS, or tang A: R:: R: cot A. XIX. The sines and cosines of two arcs, a and b, being given, it is required to find the sine and cosine of the sum or difference of these arcs. Let the radius AC=R, the árc AB-a, the arc BD=b, and consequently ABD=¿ + b. the points B and D, let fall the C FK KEP The similar triangles BCE, ICK, give the proportions, CB: CI: BE: IK, or R: cos b : sin a: IK=" CB: CI: CE: CK, or R: cos b:: cos a: CK=· sin a cos b. cos a cos b. The triangles DIL, CBE, having their sides perpendicular, each to each, are similar, and give the proportions, CB: DI :: CE : DL, or R : sin b :: cos a: DL= cos a sin b.. R CB: DI: BE: IL, or R : sin b:: sin a: But we have IK+DL=DF=sin (a+b), and CK-IL=CF÷cos (a+b). The values of sin (a-b) and of cos (a-b) might be easily deduced from these two formulas; but they may be found directly by the same figure. For, produce the sine DI till it meets the circumference at M; then we have BM=BD=b, and MI=ID=sin b. Through the point M, draw MP perpendicular, and MN parallel to, AC: since MIDI, we have MN =IL, and IN-DL. 'But we have IK-IN-MP-sin (a-b), and CK+MN=CP=cos (a-b); hence

s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510427.16/warc/CC-MAIN-20230928162907-20230928192907-00470.warc.gz

CC-MAIN-2023-40

http://koreascience.or.kr/article/JAKO200717317773034.page

math

- Volume 8 Issue 2 Speed Sensorless Vector Control of Induction Motor Using MATLAB/SIMULINK and dSPACE DS1104 MATLAB/SIMULINK와 dSPACE DS1104를 이용한 유도 전동기의 속도 센서리스 벡터제어 - Published : 2007.04.30 This paper presents a implementation of speed sensorless vector control of induction motor using MATLAB/SIMULINK and dSPACE DS1104. Proposed flux estimation algorithm, which utilize the combination of the voltage model based on stator equivalent model and the current model based on rotor equivalent model, enables stable estimation of rotor flux. Proposed rotor speed estimation algorithm utilizes the estimated flux. And the estimated rotor speed is used to speed control of induction motor. Overall system consists of speed controller, current controller, and flux controller using the most general PI controller. Speed sensorless vector control algorithm is implemented as block diagrams using MATLAB/SIMULINK. And realtime control is performed by dSPACE DS1104 control board and Real-Time-Interface(RTI). Speed Sensorless Vector Control;Induction Motor;MATLAB/SIMULINK;dSPACE

s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251696046.73/warc/CC-MAIN-20200127081933-20200127111933-00309.warc.gz

CC-MAIN-2020-05

https://www.wyzant.com/resources/answers/percentages?f=new-answers

math

An airplane left Atlanta with 52 empty seats. If the airplane was 75% full, what was the total number of seats on the airplane? Five people are to 111 bananas, two are to receive 40% each of them, two are to receive 5% each of them, and one is to receive 10% of them; how many bananas will each person get? There are no results for Only party A and Party B contested an election. All the people who are eligible to vote in an election are called the electorate. In this election, 10% of the electorate did... I just need to know how to set the equation up and the reasoning behind it. Brian invests £1200 into a savings account. The bank gives 3% compound interest for the first 2 years and 5% thereafter. How much will Brian have after 6 years to the nearest pound? The population of a certain town grows by 1.8% each year. If the population today is 62397, what will the population be in 11 years? I have a choice of answers 9.8%, 11%, 342.2, 10.2 what i have understood up till here is that A is 1/4 less than The answer provided is 41.7% but that doesn't seem correct Like 50% out of 100% is 75%, & 75% out of 100% is 87%, so what is 65% out of 100%, is it 85%. I need help on this, we are working on percentages and stuff in class. I tried to solve this and I got the answer 70%, which I know is wrong. I have no clue how to find this answer. My teacher gave it to me as a practice problem please help. step by step would be helpful I think the answer is 18.5185, but I want to know if I got it right. I don’t have anyone to ask that knows how to do this. Allyson answers 24% of her math problem in 30 minutes. She still has 10 math problems left. How many homework problems has Allyson already completed? Working at the same rate, how many more minutes... I just wanna know If 151 hours and 21 minutes is 6%, what is 20%? I do not know what the percentage is Maths question for sociology essay

s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812855.47/warc/CC-MAIN-20180219231024-20180220011024-00097.warc.gz

CC-MAIN-2018-09

https://pleasantplainsdental.com/read/an-introduction-to-dirac-operators-on-manifolds

math

By Jan Cnops Dirac operators play an immense position in numerous domain names of arithmetic and physics, for instance: index concept, elliptic pseudodifferential operators, electromagnetism, particle physics, and the illustration conception of Lie teams. during this basically self-contained paintings, the fundamental rules underlying the concept that of Dirac operators are explored. beginning with Clifford algebras and the basics of differential geometry, the textual content specializes in major homes, specifically, conformal invariance, which determines the neighborhood habit of the operator, and the original continuation estate dominating its worldwide habit. Spin teams and spinor bundles are lined, in addition to the kinfolk with their classical opposite numbers, orthogonal teams and Clifford bundles. The chapters on Clifford algebras and the basics of differential geometry can be utilized as an advent to the above themes, and are compatible for senior undergraduate and graduate scholars. the opposite chapters also are obtainable at this point in order that this article calls for little or no prior wisdom of the domain names lined. The reader will gain, despite the fact that, from a few wisdom of complicated research, which provides the best instance of a Dirac operator. extra complex readers---mathematical physicists, physicists and mathematicians from assorted areas---will get pleasure from the clean method of the speculation in addition to the hot effects on boundary worth theory. Read or Download An Introduction to Dirac Operators on Manifolds PDF Similar differential geometry books For the reason that 1994, after the 1st assembly on "Quaternionic buildings in arithmetic and Physics", curiosity in quaternionic geometry and its functions has persevered to extend. development has been made in developing new periods of manifolds with quaternionic buildings (quaternionic Kaehler, hyper Kaehler, hyper-complex, etc), learning the differential geometry of unique periods of such manifolds and their submanifolds, knowing kinfolk among the quaternionic constitution and different differential-geometric constructions, and likewise in actual purposes of quaternionic geometry. Singular areas with higher curvature bounds and, particularly, areas of nonpositive curvature, were of curiosity in lots of fields, together with geometric (and combinatorial) staff thought, topology, dynamical structures and likelihood conception. within the first chapters of the booklet, a concise creation into those areas is given, culminating within the Hadamard-Cartan theorem and the dialogue of the best boundary at infinity for easily attached whole areas of nonpositive curvature. The quantity develops the principles of differential geometry in an effort to comprise finite-dimensional areas with singularities and nilpotent features, on the comparable point as is general within the basic concept of schemes and analytic areas. the speculation of differentiable areas is constructed to the purpose of delivering a handy gizmo together with arbitrary base alterations (hence fibred items, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by means of activities of compact Lie teams and a conception of sheaves of Fr? This memoir is either a contribution to the speculation of Borel equivalence relatives, thought of as much as Borel reducibility, and degree conserving staff activities thought of as much as orbit equivalence. right here $E$ is related to be Borel reducible to $F$ if there's a Borel functionality $f$ with $x E y$ if and provided that $f(x) F f(y)$. - Initiation to Global Finslerian Geometry - Real and complex singularities : Sao Carlos Workshop 2004 - Comprehensive Introduction To Differential Geometry, 2nd Edition, Volume 4 - Differential Forms in Geometric calculus - Elegant Chaos: Algebraically Simple Chaotic Flows - Fat manifolds and linear connections Extra info for An Introduction to Dirac Operators on Manifolds A)]k = e;/Ca)(eM(a) . (a)]k) everywhere, for all k > O. In general, the mapping b ~ e:\:/(a)(eM(a) . b) defines the orthogonal projection of a Clifford number b E a p,q having zero scalar part onto the Clifford algebra generated by TaM. It is assumed here that the function! is defined on the whole of the manifold; if this is not the case, ! is silently extended to M with zero. A vector-valued Clifford field is also called a tangent vector field. 2. Derivatives and differentials 31 In the language of bundles on abstract manifolds a Clifford field is also called a section of the Clifford bundle (see the appendix), or a Clifford section for short. Finally we construct the spinor connection, which again is a slightly modified derivative. 57) Embedded spin structure. An isometric embedding in some (pseudo-)Euclidean space was sufficient to define Clifford fields in terms of functions with values in the embedding Clifford algebra. If we want to introduce spin structures we shall need a much stronger condition. This will mean a loss of generality. However, the results and properties stated here will be valid in the general case, unless stated otherwise, and can be obtained by methods quite similar to the ones used here to derive them. There also is a certain amount of arbitrariness, as is usual with square roots. We have to fix the spinor space in a certain reference point before we can define the spinor sections. But we do not want the choice to be too big, and for that we need to introduce a spin structure. This is the description of all Chapter 2. Manifolds 50 possible isomorphisms (as spinor spaces) from the spinor space in an arbitrary point of the manifold to a canonical spinor space, for which we choose the spinor space of the reference point. An Introduction to Dirac Operators on Manifolds by Jan Cnops

s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823516.50/warc/CC-MAIN-20181210233803-20181211015303-00092.warc.gz

CC-MAIN-2018-51

https://www.jiskha.com/display.cgi?id=1333814761

math

posted by Nancy . The amount of time a bank teller spends with each customer has a population mean of 3.10 minutes and standard deviation of 0.40 minute. If a random sample of 16 customers is selected, a) what assumption must be made in order to solve parts (b) and (c)? b) what is the probability that the average time spent per customer will be at least 3 minutes? c) there is an 85% chance that the sample mean will be below how many d) If a random sample of 64 customers is selected, there is an 85% chance that the sample mean will be below how many minutes?

s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424889.43/warc/CC-MAIN-20170724162257-20170724182257-00464.warc.gz

CC-MAIN-2017-30

https://books.google.com/books/about/Finite_element_Galerkin_methods_for_diff.html?id=jlUgAQAAIAAJ&hl=en

math

What people are saying - Write a review We haven't found any reviews in the usual places. TWOPOINT BOUNDARY VALUE PROBLEMS ELLIPTIC BOUNDARYVALUE PROBLEMS 4 other sections not shown Academic Press accuracy alternating direction Anal approximate solution approximation properties assume boundary conditions boundary value problems bounded domain Bramble Chapter Ciarlet coefficients Cohen-Macaulay Cohen-Macaulay ring Comp computational convergence defined Dendy denotes described dimension Dirichlet problem discrete discrete-time Galerkin Dupont error estimates estimates are derived example exists a constant family of class finite difference finite dimensional subspace finite element method following theorem Galerkin approximation Galerkin methods Galerkin procedure H ft heat equation hence Hermite polynomials independent of h integrals interpolation iteration Lemma Let R,m linear m+l m Math Mathematical matrix nonlinear norm obtain optimal L estimates parabolic problems Partial Differential Equations partition piecewise polynomials polynomials of degree proof quadrature R-module regular local ring ring R,m satisfies shown SIAM solving space variable splines subspace subspace of H sufficiently smooth superconvergence t e 0,T techniques Thomee triangle inequality Wahlbin Zlamal

s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218187792.74/warc/CC-MAIN-20170322212947-00391-ip-10-233-31-227.ec2.internal.warc.gz

CC-MAIN-2017-13

https://golfbuzz.com/d/3732-red-hazard-pond-par-3

math

Regardless of whether the hazard has red or yellow stakes a player ALWAYS has at least two options - re teeing and this option: Drop a ball behind the water hazard, keeping the point at which the original ball last crossed the margin of the water hazard directly between the hole and the spot on which the ball is dropped, with no limit to how far behind the water hazard the ball may be dropped; Depending on the design of the hole this option may not be significantly different (or could even be worse) than re teeing. The other option with red stakes is this one: As additional options available only if the ball last crossed the margin of a lateral water hazard, drop a ball outside the water hazard within two club-lengths of and not nearer the hole than (i) the point where the original ball last crossed the margin of the water hazard or (ii) a point on the opposite margin of the water hazard equidistant from the hole. Depending on where his ball last crossed the margin of the hazard, this option may not be possible. For example, if in the situation you described it would take more than two club-lengths to get to a point on the course than was outside the hazard AND not closer to the hole, then this option may not work.

s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662552994.41/warc/CC-MAIN-20220523011006-20220523041006-00614.warc.gz

CC-MAIN-2022-21

http://chuckmaddoxwatch.blogspot.com/2004/12/ordering-japanese-speedseamaster-books.html

math

Ordering Japanese Speed/Seamaster Books on Amazon Neil (UK) Posts:Seamaster books from Japan?...... [Dec 15, 2004 - 07:11 AM} I remember somebody posting details of how to order from Amazon Japan and I gave it a go some time back but couldn't manage it due to there being no pics on the site of the books in question. I have the "Speedmaster Master book" and the "Space and watch book", can't read Japanese but find them good reference for the pics. Be grateful if somebody could explain in laymans terms how to order the "Seamaster book" or any other watch books of interest. Can they be obtained in the West?? Thanks. Here is Steve's Post on the books...

s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171171.24/warc/CC-MAIN-20170219104611-00645-ip-10-171-10-108.ec2.internal.warc.gz

CC-MAIN-2017-09

https://www.almut-scheperjans.de/ball-mill/17236/ball.html

math

- / Ball Mill Rpm Calculation Ball Mill Rpm Calculation Critical Speed Calculation Ball Mill Milling cut time Calculation Circle Milling Calculations - Both inner outer Ball Mill Cusp Height Calculation Ball Mill Effective diameter Chip Thinning Calculator Thread Milling Calculations - Both inner outer 3. Drilling Calculators Cutting Speed Calculation by material Cycle time calculation Drill point Length calculation 4. Gun. Calculating Critical Speed In A Ball Mill. ball mill operating speed mechanical operations solved problems sep 11, 2014 in a ball mill of diameter 2000 mm, 100 mm dia steel balls are being used for aug 18, 2016 ball mill rpm calculation mtm crusher the critical speed of ball mill is a mill, ball mill, ceramic ball mill critical speed formula. Ball Mill Charge Calculation A Ball Mill Critical Speed actually ball, rod, AG or SAG is the speed at which the centrifugal forces equal gravitational forces at the mill shells inside surface and no balls will fall from its position onto the shell.critical speed calculation formula of ball millBall Mill Critical Speed 911 Metallurgist. Ball Mill Critical Speed Calculator Grinding Mill China. Grinding Mill Critical Speed Calculation. Ball mill calculation grinding mill china.Critical speed of ball mill calculation india technical notes 8 grinding r p king the critical speed of the mill amp c is defined as the figure 8 3 simplified calculation of the torque required to turn a mill how to calculate charge volume in ball or rod. Ball Mill Costing Calculation Ball mill rpm calculation, introduction to the mill mit ball end mills dynamic sfpm ipm cnczone the largest . milling question i think i understand pretty well how to calculate rpm a ball end mill would require different. Photo Of Ball Mill Motor @ 1,191 rpm Parallel Gearbox with 1,191 rpm input 226 rpm output. Helical gears. Ball Mill @ 226 rpm pinion gear 18 rpm bull gear. Helical gears. Clutch between gearbox ball mill Bull gear is 2-piece split design. Critical Speed Ball Mill Calculation Calculation Of Ball Mill Critical Speed. Sep 08, 2020 Ball mill critical speed calculation ball mill rpm calculation how to calculate critical speed of ball mill ore crusher quarry crusher rock crusher rollcrusher lecture 2 slideshare 23 jan 2011 the grinding in ball mill is therefore caused due to speed at which a mill charge will centrifuge is known as the. How to calculate charge in ball mill Description Calculations for mill motor power, mill speed and media charge L = Internal length of the mill in cms. after lining. how to calculate sag mill ball charge BINQ Mining. Jan 01, 2013 TechnoMine Services, LLC. mill charge and speed. Rpm Optimal Ball Mill Ball Mill Power Calculation Stone Crusher Machine. Ball mill power calculation stone crusher machine.100 tph ball mill need kw powerball mill power calculation example 1 a wet grinding ball mill in closed circuit is to be fed 100 tph of a material with a work index of 15 and a sie distribution of 80 passing inch 6350 microns the required produ. In order to design a ball mill and to calculate the specific energy of grinding, it is necessary to have equation (s) formula for critical speed of ball mill If the actual speed of a 6 ft diameter ball mill is 25 rpm, calculate lifter face inclination angle φ, steel ball distribution curve with a lower inclination. Ball Mill Critical Speed Calculator In a ball mill of diameter 2000 mm, The critical speed of ball mill is given by, where R = radius of ball mill r = radius of ball. . what is the optimum rotation speed for a . how i calculate the optimum speed of a ball mill. what is the optimum rotation speed for a ball mill. Ball mill critical speed calculation - seshadrivaradhan.in. The calculator takes the input shaft speed and the torque required for a given load What is the ball mill critical speed and how to improve ball mill efficiency . Rod and ball mills circuit sizing method - The Cement Grinding Office. Show Critical Speed Of Ball Mill Calculation Jun 26, 2017 Ball Nose Milling Without a Tilt Angle. Ball nose end mills are ideal for machining 3-dimensional contour shapes typically found in the mold and die industry, the manufacturing of turbine blades, and fulfilling general part radius requirements.To properly employ a ball nose end mill (with no tilt angle) and gain the optimal tool life and part finish, follow the 2-step process below (see Figure 1). May 28, 2012 8.1 Calculation of Cement Mill Power Consumption 8.2 Calculation of . 3.2 Calculation of the Critical Mill Speed G weight of a grinding ball in View Open - University of the Witwatersrand. Calculation For Inclination Of Ball Mill Jul 18, 2021 Now, Click on Ball Mill Sizing under Materials and Metallurgical Now, Click on Critical Speed of Mill under Ball Mill Sizing. The screenshot below displays the page or activity to enter your values, to get the answer for the critical speed of mill according to the respective parameters which is the Mill Diameter (D) and Diameter of Balls (d) Now, enter the value appropriately and accordingly. Use the SFM and the diameter of the mill to calculate the RPM of your machine. Use the RPM, IPT, CLF and the number of flutes to calculate the feed rate or IPM. Ball End Mills. Bull Nose End Mill. Flat End Mills. Metric End Mills. Milling Bits. Miniature End Mills. Calculate Critical Speed Of Ball Mill 220.127.116.11 Ball mills. The ball mill is a tumbling mill that uses steel balls as the grinding media. The length of the cylindrical shell is usually 1–1.5 times the shell diameter ( Figure 8.11). The feed can be dry, with less than 3 moisture to minimize ball coating, or slurry containing 20–40 water by weight. All calculations are based on industry formulas and are intended to provide theoretical values. End Mill Diameter Revolutions per Minute 318.057 RPM Millimeters per Minute Solution Millimeters per Tooth (Chipload) Revolutions per Minute. Ball Mill Torque Calculation Krosline How To Calculate Rpm Of A Motor To Ball Mill. Selection Sheet - Eaton Ball mills - These mills use forged steel balls up to 5 inches Use of a clutch permits the mill motor to be The required clutch torque is calculated from the power rating of the mill motor clutch shaft rpm and an appropriate service factor. Ball mill calculation kw and rpm. BALL MILL DRIVE MOTOR CHOICES - Artec Machine Systems. ball mills, the starting torque restrictions of some of the newer mill drive configurations, and the softness. How To Calculate Ball Mill Rotational Speed Calculations The critical speed of ball mill is given by, where R = radius of ball mill r = radius of ball. For R = 1000 mm and r = 50 mm, n c = 30.7 rpm. But the mill is operated at a speed of 15 rpm. Therefore, the mill is operated at 100 x 15 30.7 = 48.86 of critical speed. If 100 mm dia balls are replaced by 50 mm dia balls, and the. Milling Speed and Feed Calculator. Determine the spindle speed (RPM) and feed rate (IPM) for a milling operation, as well as the cut time for a given cut length. Milling operations remove material by feeding a workpiece into a rotating cutting tool with sharp teeth, such as an end mill or face mill. Ball Mill Parameter Selection & Calculation Ball Mill Parameter Selection Calculation Power . 30 08 2019 Critical Speed_ When the ball mill cylinder is rotated, there is no relative slip between the grinding medium and the cylinder wall, and it just starts to run in a state of rotation with the cylinder of the mill This instantaneous speed of the mill is as follows N0 — mill working speed, r min K’b — speed ratio, There are. Jul 30, 2010 The RPM for a 0.500 would be 2400 RPM. 4 300 0.500 =2400 For drilling I use an exception of 50 , so 1200 RPM. But plunging any endmill directly into the material is hard. You basicly have to slow it down till it stops chattering or the chatter is exceptable. Drilling a hole first would help a lot.

s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573760.75/warc/CC-MAIN-20220819191655-20220819221655-00572.warc.gz

CC-MAIN-2022-33

https://e2e.ti.com/support/data-converters-group/data-converters/f/data-converters-forum/1191313/tsw1400evm-time-out-error?tisearch=e2e-sitesearch&keymatch=TSW1400EVM

math

Other Parts Discussed in Thread: ADC3442EVM, I am trying to use tsw1400evm with ADC3442EVM. An error is occurring, so I am writing to get help. 1. Error message 2. A picture showing the connection of TSW1400EVM and ADC3442EVM 3. A picture of the sine signal and trigger signal being used I upload the file together. can i know the solution?

s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945279.63/warc/CC-MAIN-20230324082226-20230324112226-00555.warc.gz

CC-MAIN-2023-14

http://emilyrenee.blogspot.com/2004/09/by-numbers.html

math

A run down of my day, in numbers, but no particular order... 82-the number of steps I take between my desk and the nearest bathroom (one way) 4-the number of times I've had to use the bathroom today 2-the number of the stall in the above mentioned bathroom I always use 48-the number of hours until my friend Annie is a married woman 36-the number of hours until I'm sitting at an airport waiting to get on a plane to New York 6740-the number of inactive people just sitting in our church database 7-the number of hearts on the necklace I wear every day 12-the number of years between Cameron and myself 4-the number of notes being played wrong by the person playing the saxophone downstairs 57-the number of cars in the funeral procession I got behind on my way to the bank this afternoon. 26-the number of years rene has been alive as of today 8-the number of times I will have gone downstairs to deliver pieces of paper to people today 14-the number of months Tim and I have been together, as of tomorrow 20,000-the approximate number of characters in "Power of State," the book I am working on writing. 28-the number of junk emails I have received while sitting at my desk today 10-the number of work hours before vacation 1-the number of hours before the day is over for me

s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866326.60/warc/CC-MAIN-20180524131721-20180524151721-00420.warc.gz

CC-MAIN-2018-22

https://projecteuclid.org/journals/annals-of-statistics/volume-6/issue-1/Maximum-Likelihood-Estimation-of-Dose-Response-Functions-Subject-to-Absolutely/10.1214/aos/1176344069.full

math

Statistical properties are derived for maximum likelihood estimates of dose-response functions in which the response probability is related to the dose by means of a polynomial of unknown degree with nonnegative coefficients. Dose-response functions of this form are predicted by the multistage model of carcinogenesis. We first establish necessary and sufficient conditions for strong consistency of the estimates. For these results no assumptions are made about the polynomial degree, so the number of coefficients to be estimated is effectively infinite. Under some additional assumptions, which do involve restrictions on the polynomial degree, we obtain the asymptotic distribution of the vector of maximum likelihood estimates about the true vector of polynomial coefficients. Because the coefficients are constrained to be nonnegative, the limiting distribution will generally not be normal. "Maximum Likelihood Estimation of Dose-Response Functions Subject to Absolutely Monotonic Constraints." Ann. Statist. 6 (1) 101 - 111, January, 1978. https://doi.org/10.1214/aos/1176344069

s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572515.15/warc/CC-MAIN-20220816181215-20220816211215-00197.warc.gz

CC-MAIN-2022-33

http://patents.stackexchange.com/questions/tagged/novelty+us20070091093

math

Ask Patents Meta to customize your list. more stack exchange communities Start here for a quick overview of the site Detailed answers to any questions you might have Discuss the workings and policies of this site Idea that is similar but not identical to an existing patent: how do I evaluate the novelty? I came up with an idea similar to this one (us20070091093) around the same time and I've read this patent pretty thoroughly. They cover a large part of what my idea is, but I have differences in ... Jan 7 '13 at 19:40 newest novelty us20070091093 questions feed Announcing The Launch Of Meta Stack Exchange View patent us20070091093 Search patents with Google Clickable Video Hyperlink Apr 26, 2007 May 22, 2006 Oct 14, 2005 Hot Network Questions What are some creative ways to run up my credit card bill without any cost to me? How can I create loopable bounces for video games? Just found out my 13 year old girl is Bi and dating a 17 year old girl in an "open" relationship. Huh? Now what? Guest User "Record Create Task" Permissions Force latex to show a square matrix as square Inserting a sentence at the top of the page Collective term for data sizes (bytes, kilobytes, megabytes etc.) Good Textbooks for Real Analysis and Topology. bridge does not forwarding packets centos Intelligently Numbering "remarks" only when multiple are made Does `sl` ever show the current directory? Help with radius of convergence of a power series. Which complete lattices arise as images of the Galois connections induced by binary relations? What is the difference between 假如 and 例如? How big of a deal is Westeros? Is it OK for an MSc Student to Review a Scientific Paper? Output Pi without math How do I post a node that has its created field set to the past in a test class? Why does a nuclear explosion have directionality? Why are faces of meshes transparent in edit mode in Blender 2.69 What is Overmodulation? Are there 3 trig functions or are there 6 trig functions? Is the term 'Invalid' applicable for human beings? more hot questions Life / Arts Culture / Recreation TeX - LaTeX Unix & Linux Ask Different (Apple) Geographic Information Systems Science Fiction & Fantasy Seasoned Advice (cooking) Personal Finance & Money English Language & Usage Mi Yodeya (Judaism) Cross Validated (stats) Theoretical Computer Science Meta Stack Exchange Stack Overflow Careers site design / logo © 2014 stack exchange inc; user contributions licensed under cc by-sa 3.0

s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609537754.12/warc/CC-MAIN-20140416005217-00353-ip-10-147-4-33.ec2.internal.warc.gz

CC-MAIN-2014-15

http://www.ehow.com/how_5697310_calculate-stock-profit.html

math

When you sell shares of stock you’ve invested in, you naturally want to know how much money you made. In addition, you need to calculate stock profit because the IRS will also want to know. However, how you calculate stock profit depends in part on what your purpose is. You’ll use one method to figure your gross profit ad another to find the capital gain that is subject to income taxes. It’s important to keep careful records of each stock transaction so that you can make accurate calculations. Things You'll Need - Stock transaction records Determine the amount of money you invested. Add all purchase and transaction fees to the amount originally paid for the stock. If you paid $2,500 and had $100 in transaction fees, this gives you a total investment of $2,600. Figure your gross stock profit. First, add any dividends taken in cash to the amount you received from the sale of the stock. Then subtract your total investment. For example, suppose you sold the stock in Step 1 for $3,000 and also had $200 in dividends taken in cash rater than being reinvested, giving you a total amount received of $3,200. Subtracting the total investment of $2,600 leaves a gross profit of $600. Find the cost basis (also called tax basis) for figuring profit subject to capital gains taxes. To do this, add any reinvested dividends (but not dividends taken in cash) to your total investment in Step 1. If the total investment was $2,600 and you reinvested $200 in dividends, your tax basis works out to $2,800. Convert gross stock profit to a percentage by dividing the dollar amount of gross profit by the total investment and multiply by 100. In the above example, you would divide $600 by $2,600 to get 0.231. Multiplied by 100 you get 23.1 percent stock profit. Calculate capital gains by subtracting the tax basis from the amount received from the sale of the stock. If you sold the stock for $3,000 and the tax basis is $2,800, the stock profit subject to capital gains tax is $200.

s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886120194.50/warc/CC-MAIN-20170823113414-20170823133414-00147.warc.gz

CC-MAIN-2017-34

https://scholar.archive.org/search?q=A+Method+for+Displaying+the+Intersection+Curve+of+Two+Quadric+Surfaces.

math

A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL. The file type is Levin's method produces a parameterization of the intersection curve of two quadrics in the form where a(u) and d(u) are vector valued polynomials, and s(u) is a quartic polynomial. ... enhanced version of Levin's method is proposed that, besides classifying the morphology of the intersection curve of two quadrics, produces a rational parameterization of the curve if the curve is singular ... We thank Professor Helmut Pottmann and the referee for their helpful comments. We also thank Barry Joe for commenting on an earlier version of the paper. ...doi:10.1016/s0167-8396(03)00081-5 fatcat:dr3pbke2lvbybjpw4vwxbx4t5i Curves and Surfaces in Computer Vision and Graphics Algorithms are presented for constructing G t continuous meshes of degree two (quadric) and degree three (cubic) implicitly defined, piecewise algebraic surfaces, which exactly fit any given collection ... of points and algebraic space curves, of arbitrary degree. ... It follows then from Bezout's theorem 3.1 for surface intersection, that the two quadrics 51 and 52 must meet in a plane curve (either an irreducible conlc or straight lines). ...doi:10.1117/12.19736 fatcat:64kdqd4m65gfjorjr7m7ltv3ye This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. ... A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. ... This work was supported by the 973 Program of China (Grant No. 2004CB719404) and the Program for New Century Excellent Talents in University (Grant No. NCET-04-0088). ...doi:10.1016/j.cad.2006.04.009 fatcat:h4gws3ywkbh5vgmwwweq4x5ggq Algebraic Geometry and its Applications In this short article we summarize a number of recent applications of constructive real algebraic geometry to geometric modelling and robotics, that we have been involved with under the tutelage of Abhyankar ... The three surface intersection points are shown as the common intersections of the space curves for each pair of surfaces. ... Here we consider constructive methods for both local and global real parameterizations of curves and surfaces. ...doi:10.1007/978-1-4612-2628-4_25 fatcat:wuqw3apqqnfdnmvt5xe5s7fdxa (F-ANGR) 87c:14063 Théoréme de Torelli affine pour les intersections de deux quadriques. [The affine Torelli theorem for intersections of two quadrics] Invent. Math. 80 (1985), no. 3, 375-416. ... The main result of this paper deals with affine complete intersections U of two quadrics in affine space of even dimension. ... The number of hyperpolygons use d are optimal, in that they are the order of the minimu m number required for a smooth Gouraud like shading o f the hypersurfaces . ... Abstrac t Algorithms are presented for polygonalizing implicitl y defined, quadric and cubic hypersurfaces in n > 3 dimensional space and furthermore displaying their projections in 3D . ... Acknowledgements : I sincerely thank Insung Ihm an d Andrew Royappa for the many hours they spent in fron t of the graphics workstation, helping me visualize in fou r and higher dimensional space . ...doi:10.1145/91385.91428 dblp:conf/si3d/Bajaj90 fatcat:fpdkcsjxmndt5lol3knwo4q4a4 Constraint evaluation results in the activation of methods which compute rigid motions from surface information. ... The order in which constraints are evaluated may also be used as a language for specifying the sequence of assembly and set-up operations. ... Closed form solution are available for parametric representation of curves of intersection between any two natural quadrics [ 11,101. Vertices may be computed by efficient numeric methods . ...doi:10.1145/319120.319129 dblp:conf/si3d/Rossignac86 fatcat:ehudqr6oknan5mfxj4avz52rbu treatment of the intersection of two quadrics is too brief and too difficult to be of greatest service. ... It seems odd that it was thought necessary to speak in such detail of quadric surfaces after developing so large a number of formulas for surfaces defined by any analytic function, but the outline of the ... Woon suggests two methods for calculating points on a quadric surface intersection curve ( QSIC). ... For non-planar intersections , the curve lies in a quadric surface which has a "base curv e" which is either a line , a parabola , a hyperbola , or an box " , which is a cube or r ectangula r par all epiped ...doi:10.1145/563274.563320 dblp:conf/siggraph/Levin76 fatcat:wmskkxqcojbuzfkaub6sx7o4v4 Woon suggests two methods for calculating points on a quadric surface intersection curve ( QSIC). ... For non-planar intersections , the curve lies in a quadric surface which has a "base curv e" which is either a line , a parabola , a hyperbola , or an box " , which is a cube or r ectangula r par all epiped ...doi:10.1145/965143.563320 fatcat:dgaptn4rwvcg7nenfxzniwpaoi Topics in Surface Modeling C k Least-Squares Approximate Surface Fit: Coustruct a real algebraic surface S, which C k -1 interpolates a collection of points Pi in m..1 and given space curves Cj in m.3 as before, with associated ... Fil wilh SlIrface Patches: Construct a mesh of real algebraic surface patches S;, which C k inlNpolaLcs a collection of points Pi in m. 3 and given space curves C j in m. 3 , with associated "IlOl'lllal ... It follows then frolll Bezout's theorem 4.1 for surface intersection, that the two quadrics 51 and S'l must meet in ,L plane curve (either an irreducible conic or straight lines). ...doi:10.1137/1.9781611971644.ch2 fatcat:pyxpssexaff6pczvuz7cy7vhxm We present the first complete, exact and efficient C++ implementation of a method for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. ... Unlike existing implementations, it correctly identifies and parameterizes all the connected components of the intersection in all cases, returning parameterizations with rational functions whenever such ... Until recently, the only known general method for computing a parametric representation of the intersection between two arbitrary quadrics was that of J. Levin . ...doi:10.1145/997817.997880 dblp:conf/compgeom/LazardPP04 fatcat:6mekaucuu5ekhod7n2ponfawme treatment of the intersection of two quadrics is too brief and too difficult to be of greatest service. ... [May, intersections. The method of Monge is given the preference, but other methods are given in outline. ...doi:10.1090/s0002-9904-1914-02513-3 fatcat:h6wigtbqyneghcp2cbvknn4t3i Individual faces of a polyhedron are replaced by low degree implicit algebraic surface patches with local support. ... This paper presents efficient algorithms for generating families of curved solid objects with boundaty topology related to an input polyhedron. ... Acknowledgements : We are grateful to Vinod Anupam, Andrew Royappa and Dan Schikore for their assistance in the implementation of the smoothing algorithms. ...doi:10.1145/142920.134014 fatcat:7whadzf2z5hnfcbmaz5cmpiu5m The conchoid surface F d of a surface F with respect to a fixed reference point O is a surface obtained by increasing the distance function with respect to O by a constant d. ... This contribution studies conchoid surfaces of quadrics in Euclidean R 3 and shows that these surfaces admit real rational parameterizations. ... Acknowledgments This work has been partially supported by the 'Ministerio de Economia y Competitividad' under the project MTM2011-25816-C02-01. ...doi:10.1016/j.jsc.2013.07.003 fatcat:fltp23pn2rcjhg3ihphfj6m2g4 « Previous Showing results 1 — 15 out of 1,456 results

s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571719.48/warc/CC-MAIN-20220812140019-20220812170019-00438.warc.gz

CC-MAIN-2022-33

https://www.whowhatwhendad.com/wiki/questions/what-are-the-sides-of-a-triangle/

math

Last Updated on September 16, 2022 In geometry, the basic shape of a triangle has two sides that are 8 inches long and 10 inches long. This property of triangles can also be applied to other shapes, including cubes, hexagons, and trapezoids. If there are more than two sides, a triangle is called a psilocylindrical polygon. It is also referred to as a right-angled triangle. Triangles have two sides of lengths 8 and 10 In geometrical terms, triangles with two sides of lengths eight and ten are called right triangles. Their sum is greater than one. They also have two sides of length six and eight. However, triangles with three sides are called degenerate triangles. In this case, the two smaller sides are equal in length. Thus, these triangles are also right triangles. However, it is important to note that the sides of degenerate triangles have different lengths and corresponding angles. To know which sides are equal in length, we first need to know which side of a triangle is longer. The length of the longest side is eight and the shortest side is ten. Therefore, the sides of triangles with two sides of lengths eight and ten are equal. However, a triangle with two sides eight and ten would have three sides of length five and four, and a triangle with three sides of length five and six would have two sides that are equal in length. In addition, a triangle with two sides of length eight and ten cannot be formed from a random set of side lengths. It must have a third side whose sum is greater than eight and ten. For example, a triangle with two sides of length eight and ten is not a right triangle. The missing side can have any length between eight and ten, as long as it is shorter than eight. Angles measure 90 degrees, 30 degrees, and 100 degrees The angles are measured in degree units. An angle has several different types. A right angle, as its name suggests, is 90 degrees. This angle is often represented by a square box in between the angles’ arms. There are also other types of angles, known as obtuse angles or reflex angles. Obtuse angles measure less than 180 degrees while reflex angles exceed 360 degrees. Common examples of reflex angles are 180deg, 220deg, and 350deg. Besides being important to science, angles are also used in our everyday lives. Athletes use angles to improve their performance, whether it’s passing a soccer ball or spinning a disc to make it fly far. We use angles to measure our body rotation in sports. In discus throwing, we need to rotate at a specific angle to hit the disc far. In soccer, we need to use a certain angle to pass the ball. Although degrees are the most common unit of measurement, you can also measure angles in seconds and minutes. Usually, a degree equals 60 seconds or 60 minutes. To measure an angle, position the protractor at its vertex, where both sides of the angle meet. If you are unsure of where to place the vertex of an angle, measure it again until you find the correct number. Another way to calculate the angle measurement is to draw a triangle. A triangle has three angles, one is equal and the third is equal. The sum of all the angles in a triangle should equal 180 degrees. The same principle applies to angles in a right triangle. If the angle measurement is unknown, use an equals sign to find the value. Using a triangle’s properties, you can solve angles in three different ways. First, you must draw a triangle. Next, label the angles so that you can easily find the angles by degrees. They have two sides of lengths 5 and 8 A triangle has two sides of lengths 5 and 8, and a side of length 7. Likewise, a triangle has two unequal sides. If one side is seven inches long and the other is eight inches long, the side with the largest measurement must be longer than the other. If neither of the two sides is long enough to reach the missing side, the triangle is not a triangle. It is possible, however, for a triangle to have three sides of equal lengths. The minimum value of the third side of a triangle must be greater than the minimum value of the other two sides. However, a triangle does not contain a third side if it contains two sides of lengths of five and eight. That’s why a triangle with three sides of five and eight sides is not a triangle. The minimum and maximum value of this third side must be greater than the sum of the two sides. They have two sides of lengths 5 and 8 inches A triangle has two sides of lengths 5 and 8. The sides must be equal in length to make a right-angled triangle. This is not always the case, though. If the two shorter sides are equal in length, the triangle will have one side of length 8 inches longer than the other side. Therefore, the area of a triangle with two sides of length 5 and 8 inches is six square units. About The Author Pat Rowse is a thinker. He loves delving into Twitter to find the latest scholarly debates and then analyzing them from every possible perspective. He's an introvert who really enjoys spending time alone reading about history and influential people. Pat also has a deep love of the internet and all things digital; she considers himself an amateur internet maven. When he's not buried in a book or online, he can be found hardcore analyzing anything and everything that comes his way.

s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500288.69/warc/CC-MAIN-20230205193202-20230205223202-00093.warc.gz

CC-MAIN-2023-06

http://www.mywordsolution.com/question/formulate-the-given-dilemma-as-a-linear/9917

math

problem 1: Melissa Bakery is preparing for the coming thanksgiving festival. The bakery plans to bake and sell its favorite cookies; butter cookies, chocolate cookies and almond cookies. A kilogram of butter cookies needs three cups of flour, one cup each of special ingredient and choc chip. A cup of special ingredient is added to five cups of flour altogether with three cups of choc chic to bake a kilogram of chocolate cookies. For baking a kilogram of almond cookies; Melissa needs four cups of flour, a cup of special ingredient and two cups of choc chip. Though, each day the bakery can only allocate at most 400 cups of flour, 100 cups of special ingredient and 210 cups of choc chip to bake the cookies. Melissa estimates a daily profit of RM10 for butter cookies, RM20 for chocolate cookies and RM15 for almond cookies. The bakery wishes to maximize the daily profit. a) Formulate the given dilemma as a linear programming problem. b) The given is the final simplex tableau for the above problem: • Set up the initial simplex tableau for the above problem. • How many kilograms of each cookie should be baked? • Find out the value of m? • Identify any ingredient which is not fully utilized. State the amount unused. • How would the optimum solution change if the RHS value for the first resource rises by 10 units? problem 2: The Maju Supermarket stocks Munchies Cereal. Demand for Munchies is 4,000 boxes per year and the super market is open all through the year. Each box costs $4 and it costs the store $60 per order of Munchies, and it costs $0.80 per box per year to keep the cereal in stock. Once an order for Munchies is placed, it takes 4 days to receive the order from a food distributor. a) Find out the optimal order quantity. b) Find out the total inventory cost related with the optimal order quantity. c) What is the reorder point? d) What is the cycle time? a) A company has three factories A, B and C which supply units to warehouses X, Y and Z every month. The capacities of the factories are 60, 70 and 80 units at A, B and C correspondingly. The requirements of X, Y and Z per month are 50, 80 and 80 units correspondingly. Transportation costs per unit in ringgits are provided in the given table. How many units must ship from each factory so that the total cost is minimum? Use VAM technique for the initial solution and Stepping Stone method to get an optimal solution. b) The Dean of the Faculty of Science at City Science University has decided to apply the Hungarian method in assigning lecturers to courses for the next semester. As a criterion for judging who must teach each course, the Dean reviews the past two years teaching evaluations (which were filled out by students). As each of the four lecturers taught each of the four courses at one time or another throughout the two-year period, the Dean is able to record a course rating for each lecturer. These ratings are described in the table below. Find the best assignment of lecturers to courses to maximize the on the whole teaching rating. problem 4: The project of building a backyard swimming pool comprises of eight main activities and has to be completed within19 weeks. The activities and related data are given in the table shown below: a) Draw a network diagram for this problem. b) Find out the critical path and the expected project completion time.

s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189771.94/warc/CC-MAIN-20170322212949-00399-ip-10-233-31-227.ec2.internal.warc.gz

CC-MAIN-2017-13

http://www.commens.org/dictionary/entry/quote-letters-william-james

math

The Commens Dictionary Quote from ‘Letters to William James’ There are two kinds of Deduction; and it is truly significant that it should have been left for me to discover this. I first found, and subsequently proved, that every Deduction involves the observation of a Diagram (whether Optical, Tactical, or Acoustic) and having drawn the diagram (for I myself always work with Optical Diagrams) one finds the conclusion to be represented by it. Of course, a diagram is required to comprehend any assertion. My two genera of Deductions are first those in which any Diagram of a state of things in which the premisses are true represents the conclusion to be true and such reasoning I call Corollarial because all the corollaries that different editors have added to Euclid’s Elements are of this nature. Second kind. To the Diagram of the truth of the Premisses something else has to be added, which is usually a mere May-be, and then the conclusion appears. I call this Theorematic reasoning because all the most important theorems are of this nature.

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100674.56/warc/CC-MAIN-20231207121942-20231207151942-00874.warc.gz

CC-MAIN-2023-50

https://www.snipperoo.com/essay/logic-10

math

Professor Barbara Viola After evaluating the game of “Guess your Card”, I assume that my cards could only be 4, 5, and 9. I came up with this logic by starting with Andy. I add all three numbers together from each player. Andy has the cards of 1, 3, and 7 with a sum of 11. Belle has the cards 3, 4, and 7 with a sum of 14, ...view middle of the document... Next, Belle draw the question card, “of the five odd numbers”, how many different odd numbers do you see? She answer all of them. Only because the only odd numbers she see is from Andy and Carol which are 1, 3, and 7. That's how I came up with the numbers of 5 and 9. I then, add together 5 and 9 which is 14, let's not forget in the beginning I said the sums must add up to either 14 or 18. Since 5+9=14, and the smallest card is 1 so my cards must add up to more than 14. The sum of my cards must be 18. In order for me to find out what is my final card I must subtract 18 from 9 and 5 which gives me 4. You can also see why Andy knew what cards he had. He realize that the only odd numbers Belle could see from Carol and myself were 5 and 9, but yet she claim she could see all five odd numbers. So the remaining three: 1, 3 and 7 must have come from Andy himself. That's how he figure out what he had. The logic of “Guess your Card” is “Process of Elimination” with more possibilities being eliminated every time new information comes up.

s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574710.66/warc/CC-MAIN-20190921231814-20190922013814-00088.warc.gz

CC-MAIN-2019-39

http://mycitymychoice.com/solve-extremely-tricky-puzzle/

math

Solve This Extremely Tricky Puzzle Look at the image above and try to solve it. One honest suggestion would be to take your time before giving answer. Share this extremely tricky puzzle with your friends and family they will also enjoy it like you. To see the answer of this puzzle, please click on any social icons below. Sometime you may need to refresh the page to see them properly. Answer of the whatsapp puzzle Solve This Extremely Tricky Puzzle is : 4 How : Value of the each football from the first equation is 6 because you see 6 dots (6 + 6+ 6 = 18) From the second equation value of each wall clock is 3 because it strikes 3’O clock (3 + 3 + 3 = 9) Now the third equation is 3 x 3 – 3 = 6 value of each fan is 3 because they have three blades Now coming to the last equation it would be 2 x 3 – 2 = 4 Because Clock strikes 2 o’clock, on football you only see 3 dots/spots and fan has only 2 blades If you can solve any 3 of these 5 puzzles, you have got a great IQ - Which color will turn the bulb on? - How many differences can you find? - Can you find 4 hidden words? - How many blocks are there? - 90% can’t see the difference including Obama

s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221217951.76/warc/CC-MAIN-20180821034002-20180821054002-00515.warc.gz

CC-MAIN-2018-34

https://koasas.kaist.ac.kr/handle/10203/251654

math

We introduce a natural origin of the Peccei-Quinn (PQ) symmetry with a sufficiently good precision. In the standard model, the baryon number symmetry U(1)(B) arises accidentally due to the SU(3)(C) color gauge symmetry, and it protects the proton from a decay at a sufficient level. Likewise, if there is an SU(N) gauge symmetry in the hidden sector, an accidental hidden baryon number symmetry U(1)(BH) can appear. The hidden baryon number is solely obtained by the structure of the SU(N) group. In particular, the quality of the U(1)(BH) can be arbitrarily good for an asymptotically-free theory with large enough N. The U(1)(BH) can be identified as a PQ symmetry. Using our findings, we build two types of novel composite axion models: a model where only one SU(N) gauge symmetry is required to both guarantee the quality and break the U(1)(BH), and a model with SU(N) x SU(M) gauge symmetry where the exotic quarks responsible to the axion-gluon coupling do not confine into exotic hadrons through the dynamical breaking of the PQ symmetry, and have masses of TeV scales.

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100232.63/warc/CC-MAIN-20231130193829-20231130223829-00463.warc.gz

CC-MAIN-2023-50

https://passit.ca/real-estate-pulse/math-a-make-or-break-issue-for-some/

math

Math: A ‘Make or Break’ Issue for Some Don’t get tripped up on the first course leading to RECO salesperson registration. Math is a deciding factor for some as to whether they pass or fail the Real Estate as a Professional Career (REPC) exam. Favourite testing topics include commission calculations, statistical analysis (means, medians and modes), real estate market indicators, basic math skills, metric/imperial conversions, area measurements and mortgage math (GDS, TDS and interest calculations), capitalization, taxation and closing adjustments. Twenty-eight percent (170) of the multiple choice questions in Passit’s REPC study guide help fine tune needed math skills, emphasizing areas to review and providing feedback on progress. There’s also a math primer that covers decimal, fraction and percentage fundamentals. Don’t lose valuable marks by incorrectly converting fractions into decimals, failing to differentiate between a parallelogram and a trapazoid, or confusing the gross debt service ratio with the total debt service ratio. Here’s a classic example. Capitalization rates are used to estimate value. If the cap rate is 10.5% and the net operating income is $100,000, some students mistakenly multiply the two to arrive at value (i.e., 10.5 x $100,000 = $950,000). The correct answer: divide net operating income by the cap rate (converted to a decimal); $100,000 ÷ .105 = $952,381 (usually rounded to $952,400). Take control of math on your way to a new career.

s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202324.5/warc/CC-MAIN-20190320085116-20190320111116-00400.warc.gz

CC-MAIN-2019-13

http://mathhelpforum.com/trigonometry/80097-method-double-angle-formula-s-acceptable-test.html

math

apologies in advance, i'm quite new to these forums and don't know how to illustrate my question the proper way. i'll state my steps clearly and what i did in each step in brackets next to the equation. (Using double angle formula ) (figured out the value of ) (Moved the -1 to the left, making +1) (Divided both sides by 2) (Square root of both sides) seem correct? havn't got the answers in the back of my book. Seems right to me but i have to be sure i can use this method in my test. Would i be able to use this method for Tan, Sin, Cos and their recipricols?

s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189734.17/warc/CC-MAIN-20170322212949-00330-ip-10-233-31-227.ec2.internal.warc.gz

CC-MAIN-2017-13

https://physics.byu.edu/faculty/colton/docs/phy105-fall08/warmup26answers.html

math

If a loudspeaker emits spherical sound waves in all directions, what decreases as you go farther away from the loudspeaker? You go to a rock concert where the sound level where you are standing is 110 dB. How does the intensity (power/area) of sound waves compare to when you listen to the same music on your home stereo system, 90 dB at the spot you sit? ☐ Concert intensity = Stereo intensity ☐ Concert intensity = 1.22´ stereo intensity ☐ Concert intensity = 2´ stereo intensity ☐ Concert intensity = 10´ stereo intensity Concert intensity = 20´ stereo intensity Concert intensity = 100´ stereo intensity You hear a sonic boom: ☐ when an aircraft above you first exceeds the speed of sound ("breaks the sound barrier") ☑ whenever the aircraft flies overhead faster than the speed of sound. Ralph recently saw this bumper-sticker on a professor's car: "If this sticker is blue, you're driving too fast!" (True story: a professor at my previous university had the sticker on her car.) The sticker looks RED to him. He is confused. Can you explain the joke to Ralph? (Note: Light undergoes a Doppler effect similar to sound, although the precise equation is slightly different than the one for sound given in the textbook. Also, you need to know that red light and blue light both travel at c = 3´108 m/s, but red light has a longer wavelength than blue.) Due to the Doppler effect, frequency shifts up when an observer (the car in back of you) moves towards a source (your bumper sticker). The joke here, is that with light you would only get a shift significant enough to change red to blue when the observer is moving at a substantial fraction of the speed of light. Back to course page

s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224645417.33/warc/CC-MAIN-20230530063958-20230530093958-00415.warc.gz

CC-MAIN-2023-23

https://edform.com/worksheets/q2g7lesson-2working-with-documents-1LGEHJ

math

NAME:_________________________ DATE: GRADE 7 – ADORABLE A. DIRECTION: Define the following based on your understanding. Type your answer inside the text box. 1. What is Backstage View? 2. What is Printer Properties? B. DIRECTION: State the steps in working with documents. 1. How to Open an Existing Document 2. How to Create new Document 3. How to Save and Close a Document?

s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571538.36/warc/CC-MAIN-20220812014923-20220812044923-00684.warc.gz

CC-MAIN-2022-33

http://umj.imath.kiev.ua/article/?lang=en&article=11352

math

On the lower estimate of the distortion of distance for one class of mappings We study the behavior of one class of mappings with finite distortion in a neighborhood of the origin. Under certain conditions imposed on the characteristic of quasiconformality, we establish a lower estimate for the distortion of distance under mappings of the indicated kind. Citation Example: Markish A. A., Salimov R. R., Sevost'yanov E. A. On the lower estimate of the distortion of distance for one class of mappings // Ukr. Mat. Zh. - 2018. - 70, № 11. - pp. 1553-1562.

s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670987.78/warc/CC-MAIN-20191121204227-20191121232227-00099.warc.gz

CC-MAIN-2019-47

http://photo.stackexchange.com/tags/telephoto/new

math

New answers tagged telephoto A lens and sensor are related in size. The giant telephoto works against a sensor that is 6 times as long, and 6 times as wide, as the superzoom mini camera's sensor. The result is a lens where each element is 6 times the diameter and 6 times the thickness. Distances between teh elements are also magnified by a factor 6. And the result: 6 * 6 * 6 = 216 ... Top 50 recent answers are included

s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988650.6/warc/CC-MAIN-20150728002308-00015-ip-10-236-191-2.ec2.internal.warc.gz

CC-MAIN-2015-32

https://dsource.in/course/designing-plastic-products-injection-moulding/design-considerations/gates

math

Gate is an opening that allow melt to be injected into the mold. There are many types of gates in injection molding like sprue gate, fan gate, ring gate, standard gate, submarine gate, tab gate etc.Gate type and design depends basically on part packing, part dimension, part appearance etc. Location of the gate is also an important factor for the strength of a part. In reinforced plastic the orientation of fiber's is the factor that decides the strength of the part and the orientation of fiber's is decided by the location of injection point. If fibres are oriented in the direction of applied stress then part will have maximum strength, if fibres are oriented in a random manner then part will have a medium strength and if fibres are oriented in the direction perpendicular to the applied stress then the part will have lowest strength.

s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335004.95/warc/CC-MAIN-20220927100008-20220927130008-00359.warc.gz

CC-MAIN-2022-40

https://leagueslider.com/how-does-bh-curve-get-permeability/

math

How does BH curve get permeability? The relationship between B and H is B=μH. So if you have a B-H curve for a given material, you can find your permeability, μ, by finding B divided by H. Keep in mind that permeability is a function of H, it is not constant for all values of H. What are BH characteristics? The B-H curve is usually used to describe the magnetization properties of such materials by characterizing the permeability , which is defined as: where and represent the magnetic flux density in tesla (T) and the magnetic field intensity in ampère per meter (A/m), respectively. Which is determined by BH curve? A B-H curve plots changes in a magnetic circuit’s flux density as the magnetic field strength is gradually increased. The resulting shape indicates how the flux density increases due to the gradual alignment of the magnetic domains (atoms, that behave like tiny magnets) within the magnetic circuit material. What does the area inside the curve BH indicate? It represents how the magnetic field in the ferromagnetic material changes in accordance with the magnetic intensity. The material gets magnetized and demagnetized repeatedly which involves a loss of energy. What does permeability depend on? Permeability is largely dependent on the size and shape of the pores in the substance and, in granular materials such as sedimentary rocks, by the size, shape, and packing arrangement of the grains. How do you determine permeability? Permeability is measured on cores in the laboratory by flowing a fluid of known viscosity through a core sample of known dimensions at a set rate, and measuring the pressure drop across the core, or by setting the fluid to flow at a set pressure difference, and measuring the flow rate produced. How BH curve is drawn in magnetic circuit? The curve plotted between flux density B and magnetizing force H of a material is called magnetizing or B-H curve. The shape of curve is non-linear. This indicates that relative permeability (µr = B / µ0H) of a material is not constant but it varies. B-H curves are very useful to analyze the magnetic circuit. What is BH curve in electrical engineering? The B-H curve (or magnetisation curve) indicates the manner in which the flux density (B) varies with the magnetising force (H). (1) For non-magnetic materials. For non-magnetic materials (e.g. air, copper, rubber, wood etc.), the relation between B and H is given by. What is the relationship between B and H? In ‘free space’, the relationship between B and H is B = mu0*H, where ‘mu0’ (pronounced myoo-not) is the permeability of free space. Multiplying the magnitude of H by this number gives B – the strength of the B field is described as a flux DENSITY. How does the initial permeability of a ferromagnetic material change with magnetic strength? In ferromagnetic materials the hysteresis phenomenon means that if the field strength is increasing then the flux density is less than when the field strength is decreasing. This means that the permeability must also be lower during ‘charge up’ than it is during ‘relaxation’, even for the same value of H. Which factor depends on the permeability of the material? Permeability also depends on several factors such as the nature of the material, humidity, position in the medium, temperature, and frequency of the applied force.

s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817463.60/warc/CC-MAIN-20240419234422-20240420024422-00609.warc.gz

CC-MAIN-2024-18

https://www.bartleby.com/questions-and-answers/4.-compute-the-following-integral-by-making-a-change-in-coordinates-y-4r2y2-2y22-dz-dx-dy.-42y2-jo/99c53a76-c5c8-4ebe-8665-ce4193c49097

math

4. Compute the following integral by making a change in coordinates. ż 2 ´2 ż ? 4´y2 0 ż ? 4´x2´y2 ´ ? 4´x2´y2 x 2 a x 2 ` y 2 ` z 2 dz dx dy. Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!* Q: Find the amount of compound interest earned. 5) $5000 at 6% compounded annually for 3 years A: Recall the following fact. Q: 1 3 The image of the triangle PQR under the transformation T(x)= xis another triangle 2 3 a) Before ... A: Consider the transformation matrix: Q: Find the compound amount for the deposit. Round to the nearest cent. 4) $8000 at 6% compounded annua... A: To work out the amount earned through compound interest under the given terms A: To determine the order of the given quotient group Q: Find the vertex of the quadratic function f(x) = 3x2 24x 50 (х, у) 3 A: To determine the vertex of the (parabola) defined by the given quadratic function Q: Hi, the question is attached! I only need part iii), so don't worry about i) and ii) !!!! Thanks ? A: To determine the complex numbers z and w (change notation to avoid suffixes) satisfying the given co... Q: In Exercises 15-19 find the general solution. 15. y3y +2y e3x(1 + x) A: To find a (any) function y=y(x) satisfying the given non-homogeneous equation Q: I got this question right but how would I prove that it is divergent? I am unsure how I can break it... A: According to the divergence test, if the limit of an is not zero, or does not exist, then the sum of... Q: In Exercises 1-17 find the general solution, given that yi satisfies the complementary equation. As ... A: Given that, y1 satisfies the complementary equation.

s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046149929.88/warc/CC-MAIN-20210723143921-20210723173921-00097.warc.gz

CC-MAIN-2021-31

https://kmj.knu.ac.kr/journal/view.html?uid=2554&vmd=Full

math

Given a prime number p and a natural number m not divisible by p, we propose the problem of finding the smallest number such that for , every group G of order has a non-trivial normal p-subgroup. We prove that we can explicitly calculate the number in the case where every group of order is solvable for all r, and we obtain the value of for a case where m is a product of two primes. Throughout this note, p will be a fixed prime number. We use to denote the p-core of G, that is, its largest normal p-subgroup. We propose the following optimization problem: Given a number m not divisible by p, find the smallest r0 such that every group having order n =prm, with , has a nontrivial p-core . Denote such number r0 by . In Theorem 2.1, we will prove that is well-defined for any prime p and number m (with ). In Theorem 2.3 we explicitly determine the value of in the case that all groups whose order have the form prm are solvable (for example, if m is prime or if both p and m are odd). Finally, in Section 3, we calculate Λ(2,15), a case that is not covered by the previous theorem. We remark that the motivation for this research came from the search for examples of finite groups G such that the Brown complex of nontrivial p-subgroups of G (see for example for the definition and properties) is connected but not contractible. It is known that is contractible when G has a nontrivial normal p-subgroup, and Quillen conjectured in that the converse is also true. Theorem 2.1. For any prime number p and natural number m such that , there is a number such that if , any group of order has a non-trivial p-core . Proof. Let G be a group of order with . Let P be a Sylow p-subgroup of G. Since the kernel of the action of G on the set of cosets of P is precisely , we obtain that G embeds in Sm, and so pr divides (m-1)!. Hence, if is the largest power of p dividing ((m-1)!), we obtain that . For t,q natural numbers, let be the product (note that can also be defined as , where is the q-factorial of t), and if is a prime factorization of m, with the qi pairwise distinct and for each i, we let . We prove that if is the largest power of p dividing , then . Theorem 2.2. Let where and . If , then there is a group of order n with . Proof. Let K be the group , that is, a product of elementary abelian groups, where and are distinct primes and Cq denotes the cyclic group of order q. Then Γ(m) divides the order of , and hence so does ps. Let H be a subgroup of of order ps. For every S∈ H and k∈ K define the map by . Then is a subgroup of . If we identify H with the subgroup of maps of the form TS,0 and K with the subgroup of maps of the form , then G is just the semidirect product of K by H. Hence |G|=n. We have that G acts transitively on K in a natural fashion, and the stabilizer of 0∈ K is H, a p-Sylow subgroup of G. Hence the stabilizers of points in K are precisely the Sylow subgroups of G, so their intersection contains only the identity , as we wanted to prove. The next theorem will show that the lower bound given by Theorem 2.2 is tight in some cases. Theorem 2.3. Let , where . If G is a group of order n and ps does not divide Γ(m) then either: 1. , or 2. G is not solvable. Proof. Let G be solvable with order and . Let F(G) be the Fitting subgroup of G. Consider the map , sending g to given by conjugation by g. The restriction of c to P, a p-Sylow subgroup of G, has kernel . Since (Theorem 7.67 from ), and F(G) does not contain elements of order p by our assumption on , we have P ∩ CG(F(G))=1 and so P acts faithfully on F(G). If is the prime factorization of m, we have that F(G) is the direct product of the for . Hence . Let such that the action induced by cg on , is the identity. Since cg acts on each factor as the identity, then by Theorem 5.1.4 from , we have that it acts as the identity on each . By the faithful action of P on F(G), we have that g=1. This implies that P acts faithfully on . But then |P| divides the order of the automorphism group of , which is a product of elementary abelian groups of respective orders with for all i. Hence divides Corollary 2.4. Let ps be the largest power of p that divides . If m is prime, or if both p,m are odd, then . Proof. By Burnside's p,q-theorem, and the Odd Order Theorem, we have that all groups that have order of the form for some r are solvable. Therefore, for all , by Theorem 2.3 we have that all groups of order have non-trivial p-core. At this moment, we can prove that in some cases, the group constructed in 2.2 is unique. Theorem 2.5. Let where and s>0. If , but for all proper divisors m' of m, then up to isomorphism, the group constructed in the proof of Theorem 2.2 is the only solvable group of order n with . Proof. With the notation of the argument of the proof of 2.3, if G is a solvable group of order n with , we must have that and for all i in order to satisfy the divisibility conditions. Hence is elementary abelian and a qi-Sylow subgroup for all i, and so G is the semidirect product of a p-Sylow subgroup P of with F(G), where the action of P on F(G) by conjugation is faithful. Hence G is isomorphic to the group constructed in the proof of Theorem 2.3. One case in that we may apply Theorem 2.5 is when n=864. There are 4725 groups of order , but only one of them has the property of having a trivial 2-core. An example that cannot be tackled with the previous results is the case p=2, . In this case, . Not all groups with order of the form are solvable, however, we will prove that is actually 4. (The group S5 attests that .) Theorem 3.1. Every group G of order for r ≥ 4 is such that . Proof. Let G be a group of order for . Suppose that . From Theorem 2.3, we obtain that G is not solvable. We will prove then that . Suppose otherwise, and let T=O3(G). Then , and so G/T is solvable. Since , from Theorem 2.3, we have that . Let such that . Suppose . Since , and G/L is solvable, we have that divides , that is, . Now, L is also solvable and , hence if we had we would have , and G would have a non-trivial subnormal 2-subgroup, which contradicts our assumption that . Hence j=1. But then , which contradicts that . Hence . By a similar argument, we get that . From we obtain that G is not simple. Hence G has a proper minimal normal subgroup M. From the previous paragraph, we obtain that M is not abelian, since in that case we would have that . The only possibility is that . We have then a morphism sending g to cg, the conjugation by g. Since , and , in any case the kernel of c is a nontrivial normal 2-subgroup.

s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224653608.76/warc/CC-MAIN-20230607042751-20230607072751-00229.warc.gz

CC-MAIN-2023-23

http://www.unitedbimmer.com/forums/135325-post10.html

math

Originally Posted by mullethunter3 It factors into (2x-3)(x^4-2)=0 Meaning that the answers, by setting (2x-3) and (x^4-2) equal to zero, would be exactly 3/2... or 1.5 if you like decimals... and 2^(1/4). i.e. the forth root of 2, which makes it to be about 1.1892071150027. You so used your voyage 200 or 89.... i did... haha

s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164003787/warc/CC-MAIN-20131204133323-00032-ip-10-33-133-15.ec2.internal.warc.gz

CC-MAIN-2013-48

http://www.xavierscollege-goa.com/2019/04/30/department-of-computer-application-b-c-a-entrance-test-details/

math

Department of Computer Application (B.C.A.) St. Xavier’s College Entrance Test 2019-20 1st Round 2nd May 2019 2nd Round 3rd May 2019 (For the students who enrolled after 2nd May) Test Venue: B.C.A Lab (situated at the College lobby) Test Timing: 10.00 a.m. to 11.00. a.m. • Results of the test will be shown 30 mins. after the test ends and subsequently the admission will be confirmed of the student for the B.C.A. Programme for the academic year 2019/20. (The payment of semester fees will be on a later date which will be notified via the College website) The Fees of the entrance test will be Rs. 300 (will be collected at the Venue on the day of the entrance exam outside the B.C.A. Lab) Rules and Guide Lines 1) The test question paper contains of question in three sections a. General Aptitude b. English Language and Logical and analytical abilities c. Basic Arithmetic and statistical aptitude 2) The test questions are purely multiple choice questions (MCQs) 3) The number of questions in each section is 10 4) The total number of questions is 30 and the duration is of 1 hour . 5) Every question is of one mark each. 6) There shall be no negative marking 7) Use of calculator and other communication devices is not allowed 8) The organisers reserve the right to amend these rules as and when necessary 9) In case of any dispute the decision of the organisers will be final and binding. 30th April 2019 ________________________ Course- Co ordinator SAMPLE QUESTION PAPER FOR THE ENTRANCE TEST Section I : General Aptitude • Canine is a term referred to the species of the ______ family. a) Cow c) Cat b) Monkey d) Dog • The Eyjafjallajokul volcanic eruption happened in a) Moscow c) Ireland b) Nigeria d) Iceland • The FIFA World Cup 2022 will be held in b) South Africa • In the game of Hockey, each team has ____ players on the field at any one time a) 11 c) 9 b) 13 d) 10 • Wimbledon is associated with a) Football c) Tennis b) Basketball d) Cricket Section II : Logical Reasoning • Count the number of triangles in the following figure a) 8 c) 11 b) 9 d) 13 • Insert the missing number 857, 969, 745, 1193, ? a) 2093 c) 297 b) 1400 d) 2089 • A second is _____ fraction of an hour. a) 1/24 c) 1/60 b) 1/120 d) 1/3600 • Complete the following B G N ? F M V V a) I c)M b) P d) K • Which one does not belong to the group? a) Pencil c) Chalk b) Notebook d) Pen Section III : Basic Arithmetic Skills • The circumference of a Compact Disc can be measured as a) Πr2 c) 2Πr b) 2Πr2 d) Πr2h • Two apples and three mangoes cost Rs.86. Four apples and a mango cost Rs.112. Find the cost of an apple. a) 35 c) 20 b) 30 d) 25 • The LCM of 24, 39, 60 and 150 is a) 7800 c) 3900 b) 15600 d) 5200 • Convert 0.5% into fraction. a) 1/5 c) 1/20 b) 1/500 d) 1/200 • A train travels 82.6 km/hour. How many metres will it travel in 15 minutes? a) 20.65 c) 206.50 b) 2065 d) 20650

s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525500.21/warc/CC-MAIN-20190718042531-20190718064531-00449.warc.gz

CC-MAIN-2019-30

https://www.britannica.com/print/article/100681

math

Cavendish experiment, measurement of the force of gravitational attraction between pairs of lead spheres, which allows the calculation of the value of the gravitational constant, G. In Newton’s law of universal gravitation, the attractive force between two objects (F) is equal to G times the product of their masses (m1m2) divided by the square of the distance between them (r2); that is, F = Gm1m2/r2. The experiment was performed in 1797–98 by the English scientist Henry Cavendish. He followed a method prescribed, and used an apparatus built, by his countryman the geologist and astronomer John Michell, who had died in 1793. The apparatus featured a torsion balance: a wooden rod was suspended freely from a thin wire, and a lead sphere weighing 0.73 kg (1.6 pounds) hung from each end of the rod. A much larger sphere, weighing 158 kg (348 pounds), was placed at each end of the torsion balance. The gravitational attraction between each larger weight and each smaller one drew the ends of the rod aside along a graduated scale. The attraction between these pairs of weights was counteracted by the restoring force from a twist in the wire, which caused the rod to move from side to side like a horizontal pendulum. Cavendish and Michell did not conceive of their experiment as an attempt to measure G. The formulation of Newton’s law of gravitation involving the gravitational constant did not occur until the late 19th century. The experiment was originally devised to determine Earth’s density. Michell had likely intended to move the weights by hand, but Cavendish realized that even the smallest disturbance, such as that from the difference in air temperature between the two sides of the balance, would swamp the tiny force he wanted to measure. Cavendish placed the apparatus in a sealed room designed so he could move the weights from outside. He observed the balance with a telescope. By measuring how far the rod moved from side to side and how long that motion took, Cavendish could determine the gravitational force between the larger and smaller weights. He then related that force to the larger spheres’ weight to determine Earth’s mean density as 5.48 times that of water, or, in modern units, 5.48 grams per cubic centimetre—close to the modern value of 5.51 grams per cubic centimetre. The Cavendish experiment was significant not only for measuring Earth’s density (and thus its mass) but also for proving that Newton’s law of gravitation worked on scales much smaller than those of the solar system. Since the late 19th century, refinements of the Cavendish experiment have been used for determining G.

s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224655027.51/warc/CC-MAIN-20230608135911-20230608165911-00045.warc.gz

CC-MAIN-2023-23

https://school.gradeup.co/q61-the-radii-of-the-base-of-a-cylinder-and-a-cone-are-in-i-1njzg1

math

Q. 615.0( 1 Vote ) Given: The radii of the base of a cylinder and a cone are in the ratio 3:4. Heights of the base of a cylinder and a cone are in the ratio 2:3. Volume of cylinder is: πr2h (here r and h are radius and height of the cylinder respectively) Volume of cylinder is: πr2h Let V1 be the volume of first cylinder ∴ V1 = π(r1)2h1 Let V2 be the volume of the cone. ∴ V2 = π(r2)2h2 ∴ V1 : V2 = π(r1)2h1 : π(r2)2h2 ⇒ V1 : V2 = π × (3)2 × 2 : × π × (4)2 × 3 ⇒ V1 : V2 = 18π : × 48π = 18:16 = 9:8 ∴ V1 : V2 = 9:8 That is the ratio of their volume is 9:8. Rate this question : Two circular cylinder of equal volume have their height in the ratio 1: 2. The ratio of their radii isRS Aggarwal - Mathematics Match the following columns: The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of wire.RS Aggarwal - Mathematics 50 circular plates each of diameter 14 cm and thickness 0.5 cm are placed one above the other to form a right circular cylinder. Find its total surface area.RD Sharma - Mathematics A cylindrical bucket, 32 cm high and 18 cm of radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.RD Sharma - Mathematics Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.RD Sharma - Mathematics 25 circular plates, each of radius 10.5 cm and thickness 1.6 cm, are placed one above the other to form a solid circular cylinder. Find the curved surface area and the volume of the cylinder so formed.RD Sharma - Mathematics A path 2 m wide surrounds a circular pond of diameter 40 m. How many cubic metres of gravel are required to grave the path to a depth of 20 cm?RD Sharma - Mathematics A 16 m deep well with diameter 3.5 m is dug up and the earth from it is spread evenly to form a platform 27.5 m by 7 m. Find the height of the platform.RD Sharma - Mathematics

s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986655864.19/warc/CC-MAIN-20191015032537-20191015060037-00179.warc.gz

CC-MAIN-2019-43

https://www.shawprize.org/sc/autobiography/jeff-cheeger/

math

I was born on December 1, 1943, at the Brooklyn Jewish Hospital. I had a normal childhood, engaging in the usual games and sports. My father introduced me to mathematics at the level of elementary algebra when I was seven. Intermittently, he would teach me more. Soon I was hooked. In the seventh grade, I made a great new friend, Mel Hochster, a fellow math enthusiast, later my college roommate, now, an eminent mathematician. I attended Erasmus Hall, a large public high school with many famous alumni. There were some very bright students and the honours classes were at a good level. Eventually, I became captain of the math team. At Harvard, my teachers Shlomo Sternberg and Raul Bott were charismatic and encouraging. As a junior, with no practice, I tied for 21st in the country on the Putnam exam. This relatively modest accomplishment meant a lot to me. As a senior, I took a graduate course in PDE from a young Assistant Professor named Jim Simons. In graduate school at Princeton, after deciding to study differential geometry, I consulted Jim, who was a specialist in that area. Coincidentally, he had just moved to Princeton and was working as a code breaker at the Institute for Defense Analyses. My advisor was the legendary Salamon Bochner, but my teacher was Jim. For a year, he told me what to read and patiently answered all my questions. Then he suggested a thesis problem. After I solved it, it morphed into something very different, a finiteness theorem for manifolds of a given dimension admitting a Riemannian metric with bounds on curvature and diameter and a lower bound on volume. This needed a corresponding lower bound for the injectivity radius, which I think of as my first real theorem. The finiteness theorem brought a certain change in perspective to Riemannian geometry, now subsumed under Cheeger–Gromov compactness. The major part of my career has been spent at Stony Brook (1969–1989) and the Courant Institute (1989–). First, I spent an exciting year at Berkeley and another at Michigan. Significant stays in Brazil, Finland, IHES in France and IAS in Princeton were enormously fruitful. I have had exceptionally brilliant collaborators and some great students. Several collaborators are mentioned below. Unfortunately, space constraints forced the omission of many others. When I started doing research, my viewpoint was geometric and topological. As I learned more analysis, my work evolved into a mixture of all three fields. Several times, I noticed things which were hiding in plain sight, but which proved to have far reaching consequences. In retrospect, a significant part of my work involved finding structure in contexts which might initially have seemed too naive or too rough. Occasionally, a specific problem led to new developments that went far beyond what was needed for the original application. With strong mutual connections and the mention of a few highlights, my work could be summarized as follows. (1) Curvature and geometric analysis; see below. (2) A lower bound for the first nonzero eigenvalue of the Laplacian, which has had a vast, varied and seemingly endless number of descendants. (3) Analysis on singular spaces: The precursor was my proof of the Ray–Singer conjecture on the equality of Ray–Singer torsion, an analytic invariant and Reidemeister torsion, a topological invariant. Simultaneously, Werner Muller gave a different proof. Independently, I discovered Poincaré duality for singular spaces, in the guise of L2-cohomology. Later, I showed it was equivalent to the contemporaneously defined intersection homology theory of Goresky–MacPherson. I pioneered index theory and spectral theory on piecewise constant curvature pseudomanifolds. Applications included a local combinatorial formula for the signature. Adiabatic limits of η-invariants and local families index for manifolds with boundary were joint with Jean–Michel Bismut. (4) Metric measure spaces: I showed that properly formulated, all of first order differential calculus is valid for metric measure spaces whenever the measure is doubling and a Poincaré inequality holds in Heinonen-Koskela’s sense. Examples include non-selfsimilar fractals with dimension any real number. Related work with Bruce Kleiner and Assaf Naor had applications to theoretical computer science. Curvature. My thesis (1967) and my first paper with Detlef Gromoll (1969) on the soul theorem for complete manifolds of nonnegative curvature were purely geometric. In 1971, we proved the fundamental splitting theorem for complete manifolds of nonnegative Ricci curvature. The statement was geometric but the proof involved partial differential equations (PDE). Both works with Detlef were early examples of rigidity theorems. Here is the principle. When geometric hypotheses are sufficiently in tension, they can mutually coexist only in highly non-generic situations where specific special structure is present. Similarly, Misha Gromov and I characterized collapse with bounded curvature in terms of generalized circular symmetry (1980–1992) in the end joining forces with Kenji Fukaya (1992). Work with Toby Colding (1995–2000) on Ricci curvature was a mixture of geometry and PDE. We proved quantitative versions of rigidity theorems which, together with scaling, vastly increased their range of applicability. Specifically, if the hypotheses of rigidity theorems fail to hold by only a sufficiently small amount, then the conclusions hold up to an arbitrarily small error. Quantitative rigidity theorems were the basis of our structure theory for weak geometric limits (Gromov–Hausdorff limits) of sequences of smooth Riemannian manifolds with Ricci bounded below. These geometric objects play the role that distributions play in analysis. In particular, limit spaces can have singularities living on lower dimensional subsets and we proved a sharp bound on their dimension. Aaron Naber and I gave the first quantitative theory of such singular sets (2011–2021). Beyond bounding their dimension, we bounded their size. Our flexible techniques were rapidly applied to numerous nonlinear elliptic and parabolic geometric PDE’s. In 2015, we proved a longstanding conjecture on noncollapsed Gromov–Hausdorff limits of sequences of n-dimensional Einstein manifolds: Singular sets have dimension at most n – 4 . 28 October 2021 Hong Kong

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100909.82/warc/CC-MAIN-20231209103523-20231209133523-00529.warc.gz

CC-MAIN-2023-50

https://www.justanswer.com/boat/alhqt-ii-96-1100-yamaha-when-push-ignition-hear.html

math

Have Boat Questions? Ask a Boat Repair Expert. My name is ***** ***** am I speaking to ? Couple of things first 1.) I need the model ? 2.) Hull number if you have it ? 3.) Do you have access to a multi-meter ? 4.) Salt or fresh water ski ? 5.) Is it removed from the water, or does it sit in the water for any periods of time ?

s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824068.35/warc/CC-MAIN-20171020101632-20171020121632-00706.warc.gz

CC-MAIN-2017-43

https://www.arxiv-vanity.com/papers/1701.00796/

math

We study the energy conditions in the framework of the modified gravity with higher-derivative torsional terms in the action. We discuss the viability of the model by studying the energy conditions in terms of the cosmographical parameters like Hubble, deceleration, jerk, snap and lerk parameters. In particular, We consider two specific models that are proposed in literature and examine the viability bounds imposed by the weak energy condition. Energy conditions in gravity with higher-derivative torsion terms Tahereh Azizi 111and Miysam Gorjizadeh 222 Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-95447, Babolsar, IRAN Key Words: Teleparallel gravity, higher-derivative torsion terms, Energy conditions Recent astronomical observations [1, 2, 3] have shown that the current universe experiences an accelerated expansion. To explain this unexpected phenomenon, two remarkable approaches have been suggested. In the first approach, an exotic matter component with negative pressure is considered in the right hand side of the Einstien equations dubbed as, dark energy in the literature. There are several candidates for the dark energy proposal such as the cosmological constant , canonical scalar field (quintessence) , phantom field , chaplygin gas and so on (for a review see ). The second approach is based on the modifying the left hand side of the field equations dubbed as, dark gravity. Some examples of the modified gravity models are theories, string inspired gravity, braneworld gravity, etc ( for review see [9, 10, 11] and references therein). One of the interesting modified gravity model is the gravity which is the torsion scalar. This scenario is based on the “teleparallel” equivalent of General Relativity (TEGR) [12, 13] which uses the Weitzenböck connection that has no curvature but only torsion. Note that the Lagrangian density of the Einstien gravity is constructed from the curvature defined via the Levi-Civita connection. In the context of the TEGR, the dynamical object is a vierbein field , , which form the orthogonal bases for the tangent space at each point of spacetime. The metric tensor is obtained from the dual vierbein as where is the Minkowski metric and is the component of the vector in a coordinate basis. Note that the Greek indices are refer to the coordinates on the manifold while Latin indices label the tangent space. The Lagrangian density of the teleparallel gravity is constructed from the torsion tensor which is defined as One can write down the torsion scalar where and is the contorsion tensor defined as Using the torsion scalar as the teleparallel Lagrangian leads to the same gravitational equations of the general relativity. Similar to the modified gravity, one can modify teleparallel gravity by considering an arbitrary function of the torsion scalar in the action of the theory, which leads to the theories of gravity [14, 15, 16]. It is worth noticing that the field equations of the gravity are second order differential equations and so it is more manageable compared to the theories whose the field equations are nd order equations. Consequently, the modified TEGR models have attracted a lot of interest in literature (see and references therein ). Recently, a further modification of the teleparallel gravity has been proposed with constructing a torsional gravitational modifications using higher-derivative terms such as and terms in the Lagrangian of the theory . In this regard, the dynamical system of this model has been studied via performing the phase-space analysis of the cosmological scenario and consequently, an effective dark energy sector that comprises of the novel torsional contributions is obtained. The aim of this paper is to explore the energy conditions of this modified teleparallel gravity by taking into account the further degrees of freedom related to the higher derivative terms. Indeed, one procedure for analyzing the viability of the modified gravity models is studying the energy conditions to constrain the free parameters of them. In this respect, one can impose the null, weak, dominant and strong energy conditions ,which arise from the Raychaudhuri equation for the expansion [19, 20], to the modified gravity model. In the literature, this approach has been extensively studied to evaluate the possible ranges of the free parameter of the generalized gravity models. For instants, the energy bound have been explored to constrain theories of gravity [21, 22, 23, 24] and some extensions of gravity [25, 26, 27, 28, 29, 30, 31, 32, 33], modified Gauss-Bonnet gravity [34, 35, 36, 37] and scalar-tensor gravity [38, 39]. The energy condition have also been analysed in gravity [40, 41, 42] and generalized models of gravity [43, 44, 45, 46]. To study the energy conditions in this modified teleparallel gravity, we consider the flat FRW universe model with perfect fluid matter and define an effective energy density and pressure originates from the higher-derivative torsion terms. Then we discuss the energy conditions in term of the cosmographical parameters such as the Hubble, deceleration, jerk, snap and lerk parameters. Particularly, we consider two specific models that are proposed in literature and using the present-day values of the cosmographical parameters, we analyze the weak energy condition to determine the possible constraints on the free parameter of the presented models. The paper is organized as follows: In section 2 we review the modified gravity with higher-derivative torsion terms, the equations of motion and the resulted modified Friedmann equations related to the model. Section 3 is devoted to the energy conditions in this modified teleparallel gravity. In section 4, we explore the weak energy condition in two specific models of the scenario by using present-day values of the cosmographic quantities. Finally, our conclusion will be appeared in section 4. 2 The field equations The action of the modified teleparallel gravity with higher-derivative torsion terms is defined as where , and , and for simplicity we have set . The is the matter action includes the general matter field which can ,in general, have an arbitrary coupling to the vierbein field. If the matter couples to the metric in the standard form, then varying the action (1) with respect to the vierbein yields the generalized field equations as follows where for simplicity, we have used the notation and . Note that and denote derivative with respect to the torsion scalar and , with , respectively and is the matter energy momentum tensor which is defined as . In order to study the cosmological implication of the model, we consider a spacially flat Friedmann-Robertson-Walker (FRW) universe with metric . This metric arises from the following diagonal vierbein where is the scale factor. Now we assume that the matter content of the universe is given by the perfect fluid with the energy density and pressure . Thus using the field equations (2), we obtain the generalized Friedmann equations as follows where dot denotes the derivative with respect to cosmic time and is the Hubble parameter. With the definition of the veirbien (3), the torsion scalar and the functions and respectively are given by where the energy density and pressure of the effective dark energy sector are respectively defined as Since we have assumed a minimally coupled matter to the veirbien field, the standard matter is satisfied in continuity equation , i.e. . So from the friedmann equations (9) and (10), one can easily verified that the dark energy density and pressure satisfy the conservation equation In the rest of this paper we analyze the viability of this modified teleparallel gravity scenario by studying the energy conditions to constrain the free parameters of the model. 3 Energy conditions The energy conditions are originated from the Raychaudhuri equation together with the requirement that gravity is attractive for a space-time manifold which is endowed by a metric . In the case of a congruence of timelike and null geodesics with tangent vector field and respectively, the Raychaudhuri equation is given by the temporal variation of expansion for the respective curve as follows [19, 20, 24] Here is the Ricci tensor and , and are, respectively, the expansion scalar, shear tensor and rotation tensor associated with the congruence of timelike or null geodesics. Note that the Raychaudhuri equation is a purely geometric equation hence, it makes no reference to a specific theory of gravitation. Since the shear is a purely spatial tensor (), for any hypersurface of orthogonal congruence (), the conditions for attractive gravity reduces to where the first condition is refer to the strong energy condition (SEC) and the second condition is named null energy condition (NEC). From the field equations in general relativity and its modifications, the Ricci tensor is related to the energy-momentum tensor of the matter contents. Thus inequalities (16) give rise to the respective physical conditions on the energy-momentum tensor as where is the trace of the energy-momentum tensor. For perfect fluid with energy density and pressure , the SEC and NEC are defined by and respectively, while the dominant energy condition (DEC) and weak energy condition (WEC) are defined respectively, by and . Note that the violation of the NEC leads to the violation of all other conditions. Since the Raychaudhuri equation is a purely geometric equation, the concept of energy conditions can be extended to the case of modified theories of gravity with the assumption that the total matter contents of the universe act like a perfect fluid. Hence, the respective conditions can be defined by replacing the energy density and pressure with an effective energy density and effective pressure, respectively as follows To get some insight on the meaning of the above energy conditions, in the next section, we consider two specific functions for the Lagrangian (1), to obtain the constraints on the parametric space of the model. 4 Constraints on specific Models In order to analyze the torsional modified gravity model with higher-derivative terms from the point of view of energy conditions, we use the standard terminology in studying energy conditions for modified gravity theories. To this end, we investigate such energy bounds in terms of the cosmographic parameters , i.e. the Hubble, deceleration, jerk, snap and lerk parameters, defined respectively as where the superscripts represent the derivative with respect to time. In terms of these parameters, the Hubble parameter as well as its higher time derivatives are given by 4.1 Model I: where , and are constants. It has been shown that for a wide range of the model parameters the universe can result in a dark-energy dominated, accelerating universe and the model can describe the thermal history of the universe, i.e. the successive sequence of radiation, matter and dark energy epochs, which is a necessary requirement for any realistic scenario. Since for a theoretical model to be cosmologically viable, it should satisfy at least the weak energy condition, we examine specially the weak energy condition in our analysis. More ever, for simplicity we consider vacuum, i.e. . Inserting the cosmographical parameters (LABEL:hubble-dot) in Equ. (20), the bounds on the model parameters imposed by the weak energy condition are given by respectively. The subscript stands for the present value of the cosmographic quantities. Now, we take the following observed values for the , , , and . The numerical results for satisfying the weak energy condition are given in figure 1. For the parametric spaces of the model, we have fixed the value of to and plot the and versus and . As the figure shows, the WEC is satisfied in the specific form of Equ. (25) for a suitable choice of the subspaces of the model parametric space. 4.2 Model II: In second case, we consider a class of models in which the action does not depend on but only on given by the following functional form where , , and are constants. It has been found that in this model the universe will be led to a dark energy dominated, accelerating phase for a wide region of the parameter space. The scale factor behaves asymptotically either as a power law or as an exponential law, while for large parameter regions the exact value of the dark-energy equation-of-state parameter can be in great agreement with observations . To examine the model via energy conditions, in a similar procedure to the previous subsection, we consider the vacuum. Using the cosmographical parameters as before, the condition to justification of the WEC are obtained as

s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585381.88/warc/CC-MAIN-20211021040342-20211021070342-00427.warc.gz

CC-MAIN-2021-43

https://laserpointerforums.com/threads/actual-eye-damage-threshholds.54586/

math

- Jul 4, 2008 I was just reading a thread where some guy claimed to be a doctor, saying that an "energy density of .4 joules" causes blindness. Obviously joules is not a measurement of energy density. I am wondering how many (mw/cm^2)*time or joules/cm^2 actually causes blindness or eye damage. I haven't heard a straight answer yet.

s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506481.17/warc/CC-MAIN-20230923130827-20230923160827-00166.warc.gz

CC-MAIN-2023-40

https://demonstrations.wolfram.com/PlottingALongTimeSeries/

math

Plotting a Long Time Series Requires a Wolfram Notebook System Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products. A long time series may be better visualized using dynamic animation. This Demonstration shows the consecutive daily maximum temperature in °C from January 1, 2000 to December 31, 2005 (2192 values) for a weather station near London, Ontario. The simple fitted harmonic regression with period 365.25 is also shown. Contributed by: Ian McLeod (January 2012) (University of Western Ontario) Open content licensed under CC BY-NC-SA Deseasonalization of environmental time series using harmonic regression is discussed in . K. W. Hipel and A. I. McLeod, Time Series Modelling of Water Resources and Environmental Systems, Amsterdam: Elsevier, 1994. "Plotting a Long Time Series" Wolfram Demonstrations Project Published: January 11 2012

s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943749.68/warc/CC-MAIN-20230322020215-20230322050215-00263.warc.gz

CC-MAIN-2023-14

http://www.oceano.com/oceano/catalogo/buscador_rights.asp?IdThemRT=78&TypSearch=1&IdBook=1916&DbName=RT

math

Format: 20 x 26 cm Binding: Hardback + jacket Printing: Full colour A reference work for studying mathematics and completing self-assessment exercises with answers: the main aim is to learn, understand and apply the skills of this discipline. Arithmetic - Algebra - Geometry - Probability and Statistics Answers to Problems - Commented Problems - Mathematical Games

s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368707184996/warc/CC-MAIN-20130516122624-00034-ip-10-60-113-184.ec2.internal.warc.gz

CC-MAIN-2013-20

http://www.docsford.com/document/4563397

math

Integration by parts is used to integrate a product. The formula (given in formula book): One part of the product (u) should be easy to dvdudifferentiate (and will usually simplify when udxuvvdx，？~~dxdxdv(?differentiated). The other part should be easy ；? dx，?The other part One part is to integrate and should not become too much harder is integrated. differentiated when integrated. xCommon examination questions Definite integrals (using by parts) 2xedxExample 1: Find . ~ Example: a) Find the points where the graph of xxdxlnExample 1: Find . ~This is a suitable candidate for integration by parts ？x yxe，？(2) cuts the x and y axes. dvxThis can be found using integration by parts if we ？xwith : 2anduxe，，yxe，？(2)b) Sketch the graph of . dvdxc) Find the area of the region between the axes and take . uxx，，lnanddu？xdxyxe，？(2)22ux，，，the graph of . dxdu1 ux，，，lndvxxa) Graph cuts y-axis when x = 0, i.e. at y = 2 ，，，evedxx 2dxGraph cuts the x-axis when y = 0, i.e. when x = 2.. dvx，，，xvSubstitute these into the formula: ydx2xxxxxb) The graph looks like: 322222xedxxeedxxeec，？，？？ Substitute these into the formula: ~~ 2.5222 x1x2211？x dxxxxdx，？lnxxdxxlnln，？！22c) Area is . (2)？xedx~~~~1.52xxdxcos2Example 2: Find . x~022111 ，？？xxxcln 24du0.5，？，，？21uxdv Here we take : uxx，，andcosdxx0.511.52 dxdvlnxdxExample 2: Find . ？？xx~，，，？evedu dxux，，，1？？？xxx1lnxdxThis can be thought of as and so can be dx(2)(2)()1？，？？？？！？xedxxeedx~So ~~dv，，，cossinxvxdv？？xx？？？(2)()xeedx = integrated by parts with ux，，lnand1~dxdx？？xxSubstitute these into the formula: ？？？(2)()xee = du1xxdxxxxdxxxxccossinsinsin(cos)，？，？？？ux，，，lnNow that we’ve integrated, we substitute in our ~~ dxx limits: dv，？？xxxcsincos2，，，1vx2？？？xxx ：?(2)(2)？，？？？xedxxeedx~；(0Note: Sometimes it is necessary to use the 01？？2200 ！xdxxxdx，？ln1lnlnxdxxx，？ ，？？？？？02eeeeintegration by parts formula twice (e.g. with ;；;；~~~x2，？，0.13511.135xxdxsin). xxxcln？？~ =

s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794870470.67/warc/CC-MAIN-20180527205925-20180527225925-00061.warc.gz

CC-MAIN-2018-22

https://cameroongcerevision.com/relationship-between-intermolecular-potential-energy-and-particle-separations/

math

In this page we will are going to explore the Relationship between Intermolecular Potentail Engergy [P.E] and Particle Separations. we are also going to see how the P.E Curve to explain some properties of Material, This is a continuation of our Matter series , topic sen in the gcse and gce A level. Intermolecular potential energy [P.E] 2 molecules would repel and attract each other depending of their separation. When far apart their P.E due to interaction is 0. When close to each other, their P.E due to interaction action between them until they reach the equilibrium separation r0 where the overall force is 0 if the molecules are pushed closer the P.E increases as work is done on the repulsive forces due to the electron. Intermolecular potential energy curve Intermolecular potential energy and Particle Separations Using the Intermolecular potential energy curve to explain some properties of Material I – Surface Tension Molecules inside the liquid are at equilibrium separation ro i.e. all forces on them are O. Moles near or at the surface are more spaced out i.e. Mro and the net force on them is attractive (even though weak) this moles are thus in a state of tension thus a need i.e. can be made to lie on the surface of water. ii Hooke’s law The intermolecular force separation curve is straight at and near the equilibrium separation ro the straight nature and near ro means the separation is proportionate to the force which is hooke’s law provided the separation is not too much to cause permanent stretching. Thus hooker’s law is obeyed only within this region “Hookian region” At normal temperature the intermolecular separation is minimum which corresponds to o and ro suppose the subs is given some energy ΔU. The energy of the system = μo + ΔU Moves from μo to μ. This causes the separation of the particles to have a shift to the right of their equilibrium position. The new equilibrium position is greater the r0 r>r0 . Because of the asymmetric nature of the graph. This means the amplitude of variation of the particles increases. The net effect for all the particles increases. The net effect for all the particles that makeup the material is an increase in size of the material. Hence materials expand when heated. iv) Latent heat it can be seen from p.e separation curve that if 2 atoms are to become completely free from each other’s influence to acquire O potential energy of such. Then they need to gain an amount of energy. Thus ξ0 can be considered to be the binding energy of such a pair of atom consider a solid in which each atom has n nearest neighbors that is a coordination number of n). Since interatomic forces at short range, it can be assumed that each of the 2 atoms involve in n bond. In other for such a bond to be broken, the amount of energy that each of the atoms interact only with these n atoms that each of the 2 atoms has to acquire is ξ/2, since the change of atoms in 1 mole is numerically equal Na and each atom is involved in n bonds, the total energy require to separate the atoms of 1 mole of solid completely at absolute

s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400201699.38/warc/CC-MAIN-20200921112601-20200921142601-00598.warc.gz

CC-MAIN-2020-40

http://www.mywordsolution.com/question/what-amounts-will-appear-in-the-2014-year-end/93596

math

Chamberlain Enterprises Inc. reported the following receivables in its month December 31, 2013, year-end balance sheet: 1. The notes receivable account comprises two notes, $65,000 note and $325,000 note. The $65,000 note is dated October 31, 2013, with principal and interest payable on October 31, 2014. The $325,000 note is dated June 30, 2013, with principal and 6% interest payable on June 30, 2014. 2. Throughout 2014, sales revenue totalled $1,470,000, $1,345,000 cash was gathered from customers and $35,000 in accounts receivable was written off. All sales are made on a credit basis. Bad debt expense is recorded at year-end by adjusting the allowance account to an amount equivalent to 10% of year-end accounts receivable. 3. On March 31, 2014, the $325,000 note receivable was discounted at the Bank of Commerce. The bank's discount rate is 8%. Chamberlain accounts for the discounting as a sale. 1. In addition to sales revenue, what expense and revenue amounts related to receivables will appear in Chamberlain’s 2014 income statement? 2. What amounts will appear in the 2014 year-end balance sheet for accounts receivable? 3. Compute the receivables turnover ratio for 2014.

s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120092.26/warc/CC-MAIN-20170423031200-00049-ip-10-145-167-34.ec2.internal.warc.gz

CC-MAIN-2017-17

http://www.howtoreadachart.com/2016/12/07/rule-of-twelfths/

math

The Rule of Twelfths is a rule of thumb for estimating the height of the tide at any given time. The rate of flow in a tide increases smoothly to a maximum halfway point between high and low tide, before smoothly decreasing to zero again. This is important when navigating a boat or a ship in shallow water, and when launching and retrieving boats on slipways on a tidal shore. The rule assumes that the rate of flow of a tide increases smoothly to a maximum halfway between high and low tide before smoothly decreasing to zero again and that the interval between low and high tides is approximately six hours. The rule states that in the first hour after low tide the water level will rise by one twelfth of the range, in the second hour two twelfths, and so on according to the sequence – 1:2:3:3:2:1. If a tide table gave us the information that tomorrow’s low water would be at noon and that the water level at this time would be two meters above chart datum and further, that at the following high tide the water level would be 14 meters. We could work out the height of water at 3 p.m. as follows: * The total increase in water level between low and high tide would be: 14 – 2 = 12 meters. * In the first hour the water level would rise by 1 twelfth of the total (12 m) or: 1 m * In the second hour the water level would rise by another 2 twelfths of the total (12 m) or: 2 m * In the third hour the water level would rise by another 3 twelfths of the total (12 m) or: 3 m * This gives us the increase in the water level by 3:00 p.m. as 6 This represents only the increase – the total depth of the water (relative to chart datum) will include the 2 m depth at low tide: 6 m + 2 m = 8 meters. Obviously the calculation can be simplified by adding twelfths together and reducing the fraction beforehand. However, there is warning about when using the rule. The rule is a rough approximation only and should be applied with great caution when used for navigational purposes. Officially produced tide tables should be used in preference whenever possible. The rule assumes that all tides behave in a regular manner, this is not true of some geographical locations, such as Poole Harbour or the Solent where there are “double” high waters or Weymouth Bay where there is a double low water. The rule assumes that the period between high and low tides is six hours but this is an underestimate and can vary anyway.

s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987795253.70/warc/CC-MAIN-20191021221245-20191022004745-00407.warc.gz

CC-MAIN-2019-43

https://en.wikiversity.org/wiki/Exploratory_factor_analysis

math

Exploratory factor analysis |This page summarises key points about the use of exploratory factor analysis particularly for the purposes of psychometric instrument development. For a hands-on tutorial about the steps involved, see EFA tutorial.| Assumed knowledge[edit | edit source] Purposes of factor analysis[edit | edit source] There are two main purposes or applications of factor analysis: - 1. Data reduction Reduce data to a smaller set of underlying summary variables. For example, psychological questionnaires often aim to measure several psychological constructs, with each construct being measured by responses to several items. Responses to several related items are combined to create a single score for the construct. A measure which involves several related items is generally considered to be more reliable and valid than relying on responses to a single item. - 2. Exploring theoretical structure Theoretical questions about the underlying structure of psychological phenomena can be explored and empirically tested using factor analysis. For example, is intelligence better understood as a single, general factor, or as consisting of multiple, independent dimensions? Or, how many personality factors are there and what are they? History[edit | edit source] There are several requirements for a dataset to be suitable for factor analysis: - Normality: Statistical inference is improved if the variables are multivariate normal - Linear relations between variables - Test by visually examining all or at least some of the bivariate scatterplots: - Is the relationship linear? - Are there bivariate outliers? - Is the spread about the line of best fit homoscedastic (even (or cigar-shaped) as opposed to fanning in or out))? - If there are a large number of variables (and bivariate scatterplots), then consider using Matrix Scatterplots to efficiently visualise relations amongst the sets of variables within each factor (e.g., a Matrix Scatterplot for the variables which belong to Factor 1, and another Matrix Scatterplot for the variables which belong to Factor 2 etc.) - Factorability is the assumption that there are at least some correlations amongst the variables so that coherent factors can be identified. Basically, there should be some degree of collinearity among the variables but not an extreme degree or singularity among the variables. Factorability can be examined via any of the following: - Inter-item correlations (correlation matrix) - are there at least several small-moderate sized correlations e.g., > .3? - Anti-image correlation matrix diagonals - they should be > ~.5. - Measures of sampling adequacy (MSAs): - Kaiser-Meyer-Olkin (KMO) (should be > ~.5 or .6) and - Bartlett's test of sphericity (should be significant) - Sample size: The sample size should be large enough to yield reliable estimates of correlations among the variables: - Ideally, there should be a large ratio of N / k (Cases / Items) e.g., > ~20:1 - e.g., if there are 20 items in the survey, ideally there would be at least 400 cases) - EFA can still be reasonably done with > ~5:1 - Bare min. for pilot study purposes, as low as 3:1. - Ideally, there should be a large ratio of N / k (Cases / Items) e.g., > ~20:1 For more information, see these lecture notes. Types (methods of extraction)[edit | edit source] The researcher will need to choose between two main types of extraction: - Principal components (PC): Analyses all variance in the items. This method is usually preferred when the goal is data reduction (i.e., to reduce a set of variables down to a smaller number of factors and to create composite scores for these factors for use in subsequent analysis). - Principal axis factoring (PAF): Analyses shared variance amongst the items. This method is usually preferred when the goal is to undertake theoretical exploration of the underlying factor structure. Rotation[edit | edit source] The researcher will need to choose between two main types of factor matrix rotation: - Orthogonal (Varimax - in SPSS): Factors are independent (i.e., correlations between factors are less than ~.3) - Oblique (Oblimin - in SPSS): Factors are related (i.e., at least some correlations between factors are greater than ~.3). The extent of correlation between factors can be controlled using delta. - Negative values "decrease" factor correlations (towards full orthogonality) - "0" is the default - Positive values (don't go over .8) "permit" higher factor correlations. If the researcher hypothesises uncorrelated factors, then use orthogonal rotation. If the researchers hypothesises correlated factors, then use oblique rotation. In practice, researchers will usually try different types of rotation, then decide on the best form of rotation based on the rotation which produces the "cleanest" model (i.e., with lowest cross-loadings). Determining the number of factors[edit | edit source] There is no definitive, simple way to determine the number of factors. The number of factors is a subjective decision made by the researcher. The researcher should be guided by several considerations, including: - Theory: e.g., How many factors were expected? Do the extracted factors make theoretical sense? - Eigen values: - Kaiser's criterion: How many factors have eigen-values over 1? Note, however, that this cut-off is arbitrary, so is only a general guide and other considerations are also important. - Scree-plot: Plots eigen-values. Look for the 'elbow' minus 1 (i.e., where there is a notable drop); the rest is 'scree'. Extract the number of factors that make up the 'cliff' (i.e., which explain most of the variance). - Total variance explained: Ideally, try to explain approximately 50 to 75% of the variance using the least number of factors - Interpretability: Are all factors interpretable? (especially the last one?) In other words, can you reasonably name and describe each set of items as being indicative of an underlying factor? - Alternative models: Try several different models with different numbers of factors before deciding on a final model and number of factors. Depending on the Eigen Values and the screen plot, examine, say, 2, 3, 4, 5, 6 and 7 factor models before deciding. - Remove items that don't belong: Having decided on the number of factors, items which don't seem to belong should be removed because this can potentially change and clarify the structure/number of factors. Remove items one at a time and then re-run. After removing all items which don't seem to belong, re-check whether you still have a clear factor structure for the targetted number of factors. It may be that a different number of factors (probably one or two fewer) is now more appropriate. For more information, see criteria for selecting items. - Number of items per factor: The more items per factor, the greater the reliability of the factor, but the law of diminishing returns would apply. Nevertheless, a factor could, in theory, be indicated by as little as a single item. - Factor correlations - What are the correlations between the factors? If they are too high (e.g., over ~.7), then some of the factors may be too similar (and therefore redundant). Consider merging the two related factors (i.e., run an EFA with one less factor). - Check the factor structure across sub-samples - For example, is the factor structure consistent for males and females? (e.g., in SPSS this can be done via Data - Split file - Compare Groups or Organise Output by Groups - Select a categorical variable to split the analyses by (e.g., Gender) - Paste/Run or OK - Then re-run the EFA syntax) Mistakes in factor extraction may consist in extracting too few or too many factors. A comprehensive review of the state-of-the-art and a proposal of criteria for choosing the number of factors is presented in . Criteria for selecting items[edit | edit source] In general, aim for a simple factor structure (unless there is a particular reason why a complex structure would be preferable). In a simple factor structure each item has a relatively strong loading on one factor (target loading; e.g., > |.5|) and relatively small loadings on other factors (cross-loadings; e.g., < |.3|). Consider the following criteria to help decide whether to include or remove each item. Remember that these are rules of thumb only – avoid over-reliance on any single indicator. The overarching goal is to include items which contribute to a meaningful measure of an underlying factor and to remove items that weaken measurement of the underlying factor(s). In making these decisions, consider: - Communality - indicates the variance in each item explained by the extracted factors; ideally, above .5 for each item. - Primary (target) factor loading - indicates how strongly each item loads on each factor; should generally be above |.5| for each item; preferably above |.6|. - Cross-loadings - indicate how strongly each item loads on the other (non-target) factors. There should be a gap of at least ~.2 between the primary target loadings and each of the cross-loadings. Cross-loadings above .3 are worrisome. - Meaningful and useful contribution to a factor - read the wording of each item and consider the extent to which each item appears to make a meaningful and useful (non-redundant) contribution to the underlying target factor (i.e., assess its face validity) - Reliability - check the internal consistency of the items included for each factor using Cronbach's alpha and check the "Alpha if item removed" option to determine whether removal of any additional items would improve reliability) - See also: How do I eliminate items? (lecture notes) Name and describe the factors[edit | edit source] Once the number of factors has been decided and any items which don't belong have been removed, then - Give each extracted factor a name - Be guided by the items with the highest primary loadings on the factor – what underlying factor do they represent? - If unsure, emphasise the top loading items in naming the factor - Describe each factor - Develop a one sentence definition or description of each factor Data analysis exercises[edit | edit source] Pros and cons[edit | edit source] - Basic terms - Anti-image correlation matrix: Contains the negative partial covariances and correlations. Diagonals are used as a measure of sampling adequacy (MSA). Note: Be careful not to confuse this with the anti-image covariance matrix. - Bartlett's test of sphericity: Statistical test for the overall significance of all correlations within a correlation matrix. Used as a measure of sampling adequacy (MSA). - Common variance: Variance in a variable that is shared with other variables. - Communality: The proportion of a variable's variance explained by the extracted factor structure. Final communality estimates are the sum of squared loadings for a variable in an orthogonal factor matrix. - Complex variable: A variable which has notable loadings (e.g., > .4) on two or more factors. - Correlation: The Pearson or product-moment correlation coefficient. - Composite score: A variable which represents combined responses to multiple other variables. A composite score can be created as unit-weighted or regression-weighted. A composite score is created for each case for each factor. - Correlation matrix: A table showing the linear correlations between all pairs of variables. - Data reduction: Reducing the number of variables (e.g., by using factor analysis to determine a smaller number of factors to represent a larger set of factors). - Eigen Value: Column sum of squared loadings for a factor. Represents the variance in the variables which is accounted for by a specific factor. - Exploratory factor analysis: A factor analysis technique used to explore the underlying structure of a collection of observed variables. - Extraction: The process for determining the number of factors to retain. - Factor: Linear combination of the original variables. Factors represent the underlying dimensions (constructs) that summarise or account for the original set of observed variables. - Factor analysis: A statistical technique used to estimate factors and/or reduce the dimensionality of a large number of variables to a fewer number of factors. - Factor loading: Correlation between a variable and a factor, and the key to understanding the nature of a particular factor. Squared factor loadings indicate what percentage of the variance in an original variable is explained by a factor. - Factor matrix: Table displaying the factor loadings of all variables on each factor. Factors are presented as columns and the variables are presented as rows. - Factor rotation: A process of adjusting the factor axes to achieve a simpler and pragmatically more meaningful factor solution - the goal is a usually a simple factor structure. - Factor score: Composite score created for each observation (case) for each factor which uses factor weights in conjunction with the original variable values to calculate each observation's score. Factor scores are standardised to according to a z-score. - Measure of sampling adequacy (MSA): Measures which indicate the appropriateness of applying factor analysis. - Oblique factor rotation: Factor rotation such that the extracted factors are correlated. Rather than arbitrarily constraining the factor rotation to an orthogonal (90 degree angle), the oblique solution allows the factors to be correlated. In SPSS, this is called Oblimin rotation. - Orthogonal factor rotation: Factor rotation such that their axes are maintained at 90 degrees. Each factor is independent of, or orthogonal to, all other factors. In SPSS, this is called Varimax rotation. - Parsimony principle: When two or more theories explain the data equally well, select the simplest theory e.g., if a 2-factor and a 3-factor model explain about the same amount of variance, interpret the 2-factor model. - Principal axis factoring (PAF): A method of factor analysis in which the factors are based on a reduced correlation matrix using a priori communality estimates. That is, communalities are inserted in the diagonal of the correlation matrix, and the extracted factors are based only on the common variance, with unique variance excluded. - Principal component analysis (PC or PCA): The factors are based on the total variance of all items. - Scree plot: A line graph of Eigen Values which is helpful for determining the number of factors. The Eigen Values are plotted in descending order. The number of factors is chosen where the plot levels off (or drops) from cliff to scree. - Simple structure: A pattern of factor loading results such that each variable loads highly onto one and only one factor. - Unique variance: The proportion of a variable's variance that is not shared with a factor structure. Unique variance is composed of specific and error variance. - Common factor: A factor on which two or more variables load. - Common factor analysis: A statistical technique which uses the correlations between observed variables to estimate common factors and the structural relationships linking factors to observed variables. - Error variance: Unreliable and inexplicable variation in a variable. Error variance is assumed to be independent of common variance, and a component of the unique variance of a variable. - Image of a variable: The component of a variable which is predicted from other variables. Antonym: anti-image of a variable. - Indeterminacy: If it is impossible to estimate population factor structures exactly because an infinite number of factor structures can produce the same correlation matrix, then there are more unknowns than equations in the common factor model, and we say that the factor structure is indeterminate. - Latent factor: A theoretical underlying factor hypothesised to influence a number of observed variables. Common factor analysis assumes latent variables are linearly related to observed variables. - Specific variance: (1) Variance of each variable unique to that variable and not explained or associated with other variables in the factor analysis. (2) The component of unique variance which is reliable but not explained by common factors. References[edit | edit source] - Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4, 272–299. - Tabachnick, B. G. & Fidell, L. S. (2001). Principal components and factor analysis. In Using multivariate statistics (4th ed., pp. 582–633). Needham Heights, MA: Allyn & Bacon. - Iantovics, L.B., Rotar, C., Morar, F.: Survey on establishing the optimal number of factors in exploratory factor analysis applied to data mining, Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 9(2), 2019, e1294. See also[edit | edit source] - Lecture notes - Data analysis tutorial - Internal consistency - Composite scores - Practice quiz - Psychometric instrument development - Sample write-ups - Survey research and design in psychology - Wikipedia & Wikibooks - Exploratory factor analysis (Wikipedia) - Factor analysis in psychometrics (Wikipedia) - Principal component analysis (Wikipedia) - Principal component analysis (Wikibooks) [edit | edit source] - Darlington, R. B., Factor analysis. - Exploratory factor analysis (Lecture slides on slideshare.net) - Exploratory factor analysis (Lecture on ucspace.canberra.edu.au) - Factor analysis links (del.icio.us) - Factor analysis resources: Understanding & using factor analysis in psychology & the social sciences (Wilderdom) - Open and free online course on exploratory data analysis (Carnegie Mellon University) - Principal components and factor analysis (statsoft.com) - Factor analysis: Principal components factor analysis: Use of extracted factors in multivariate dependency models (bama.ua.edu)

s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510924.74/warc/CC-MAIN-20231001173415-20231001203415-00299.warc.gz

CC-MAIN-2023-40

https://optiwave.com/forums/reply/12207/

math

June 30, 2014 at 3:04 pm #12207 Thank you very much, that makes sense! Also, I dont known how to get the simulation result of the local electric field enhancement of gold nanorod array? As shown in the attached file (I found in a ref.), how do they get the value of E/E0?

s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506686.80/warc/CC-MAIN-20230925051501-20230925081501-00568.warc.gz

CC-MAIN-2023-40

http://www.lmfdb.org/knowledge/show/st_group.supgroups

math

The minimal supergroups of a Sato-Tate group $G$ are the groups $H$ that properly contain $G$ with finite index and do not properly contain any other proper supergroup of $G$; they necessarily have the same identity component $H^0=G^0$ as $G$. - Review status: reviewed - Last edited by Kiran S. Kedlaya on 2018-06-20 04:16:16 Referred to by:History: (expand/hide all) - 2018-06-20 04:16:16 by Kiran S. Kedlaya (Reviewed)

s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141189141.23/warc/CC-MAIN-20201127044624-20201127074624-00248.warc.gz

CC-MAIN-2020-50

http://www.solutioninn.com/peoples-energy-inc-reports-the-following-data-for-operating-revenue

math

Question: Peoples Energy Inc reports the following data for operating revenue Peoples Energy, Inc. reports the following data for operating revenue and net income for 2001–2005. Determine the least-squares regression line and interpret its slope. Estimate the net income if the operating revenue figure is $2500 million. Relevant QuestionsFor 2004 through 2008, Coca-Cola annual operating revenues and net incomes were as shown below. Determine the least-squares regression line and interpret its slope. Estimate net income if the operating revenue is $30 ...Determine the least-squares regression line for the data in Exercise 15.7, then calculate the sum of the squared deviations between y and ŷ. In exercise A scatter diagram includes the data points (x = 3, y = 8), (x = 5, y = ...For the ANOVA portion of the printout shown in Exercise 15.85, explain the exact meaning of each number in the “SS” and “F” columns. In exercise For the regression equation obtained in Exercise 15.93, analyze the residuals by (a) Constructing a histogram, (b) Using a normal probability plot, (c) Plotting the residuals versus the x values, and (d) Plotting the ...The makers of a pie crust mix have baked test pies and collected the following data on y = amount of crispness (a rating of 1 to 100), x1 = minutes in the oven, and x2 = oven temperature (degrees Fahrenheit). a. Determine ... Post your question

s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818685850.32/warc/CC-MAIN-20170919145852-20170919165852-00086.warc.gz

CC-MAIN-2017-39

http://www.barnesandnoble.com/w/immanuel-kant-m-james-ziccardi/1117939795?ean=9781494859619

math

- Shopping Bag ( 0 items ) • The limits of ... • The limits of theoretical knowledge • Kant's Copernican Revolution • The distinction between the phenomenal and the noumenal • The antinomies and dialectical logic • Synthetic a priori knowledge • Kantian ethics (deontology) • The Categorical Imperative • Kant's ideas on free will, the immortality of the soul, and the existence of God A brief biography of the life of Immanuel Kant is also included in the book.

s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678674071/warc/CC-MAIN-20140313024434-00049-ip-10-183-142-35.ec2.internal.warc.gz

CC-MAIN-2014-10

https://www.alisonxox.com/vip-specials

math

As you already know we have made a solid reputation with our duo sessions. Since we started working together as partner in crime six years ago , we know each other very well and we have the advantage of being extremely intimate and complice. That level of comfort between us is rare in the industry. As a client , your job is to simply let us lead and you will enjoy every second of it. 60 min / 440$ 90 min / 640$ 2h / 840$ 2.5h / 1040$ 3h / 1200$ As always , we are only offering safe services and all the bookings must be done with a minimum of 24h notice with a 200$ deposit.

s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00576.warc.gz

CC-MAIN-2022-49

http://muscleandbrawn.com/forum/59772-post43.html

math

Originally Posted by DieselWeasel ricka: ((Weight x Reps) x .0333) + Weight (# used in the beginning of the formula) = 1RM That's the formula which Wendler uses in his 5/3/1 ebook. It's been the most accurate out of any that I've previously used. So that calculator must use that formula..because I just did the math using (135x10= 1350 x .0333 = 44.95 + 135 = 179.95 I just did 225 10 days ago, so that formula must not work for everyone.. strange... Mt Snow, VT - May 5, 2012 - Completed! Gunstock, NH - June 1, 2013 - Completed! ...i remain, he who remains to be...

s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501173866.98/warc/CC-MAIN-20170219104613-00548-ip-10-171-10-108.ec2.internal.warc.gz

CC-MAIN-2017-09

http://mathhelpforum.com/algebra/128446-extremely-simple-log-problem-d.html

math

How Would One Go about simplifying this ln(3x^2 - 9x) + ln(1/3x) Follow Math Help Forum on Facebook and Google+ you could use this law of logarithms : . But before proceeding to this, we need a little clarification : is your second term or ? It Looks like this Then, using the law of logarithms I mentioned in my previous post, you have : Note that the top part of the fraction, , can be factored as . Therefore : Conclusion : Does this make sense ? Thank You very much very helpful View Tag Cloud

s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120844.10/warc/CC-MAIN-20170423031200-00219-ip-10-145-167-34.ec2.internal.warc.gz

CC-MAIN-2017-17

https://math.answers.com/Q/Can_you_give_me_sixty-three_dollars_using_six_pieces_no_dollars_and_no_cents

math

.95 dollars (if you are using USD) Decimals currency, meaning dollars and cents, was introduced in Australia on 14 February 1966. 2 half dollars and 4 quarters=200 cents/$2. 550 cents is equal to $5.50 Seriously !... $4.79 without using a calculator ! The subtotal is eight dollars, plus tax it's a total of eight dollars and eighty-five cents. Decimal currency was introduced in New Zealand in 1967. you would get 50 cents back or you would get a half dollar back:) There are many countries which use dollars and cents as their currency units. However, they do not have the same coinage and so, without knowing the country which this question refers o, it is not possible to give an answer. You write the dollars to the left of the decimal point; and the cents to the right, using two decimals. We know that 100 cents is the equivalent of $1. So 1000 cents would be equivalent of $10. So If 1000 cents are the same as $10 that means that 2000 cents would be $20. So now using what you see already you can determine that 6000 cents would be the same as $60.

s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104683020.92/warc/CC-MAIN-20220707002618-20220707032618-00331.warc.gz

CC-MAIN-2022-27

http://www.imgrum.org/tag/%E3%82%AF%E3%83%AD%E3%83%8A%E3%83%83%E3%83%84

math

Is it just me or are there anyone who also enjoys devouring a bunch of indulgent pastries and sweets for breakfast? More sweets from@dabjapan because their creation never disappoints.❤️ Apricot caramel and lemon sugar cronut(yes, best cronut I ever had), chocolate banana monkey Le religeusse and mentaiko focaccia in the shape of an onigiri. Can't wait for the weekend! So the cronut: it is an odd mix of a croissant and a donut. Apparently it is very technically difficult to bake as crossaint dough is very easy to burn but donuts need to be deep fried. I think it was in 2015 that I became obsessed with finding and eating the elusive cronut. They sold some crap version in Woolworths but I knew if I wanted to try the real thing I would have to go to New York. Lo, and behold there is actually not 1 but 2 Dominique Ansel bakeries in Tokyo. I went the first time last year but neglected to take a pic. This year I went again, and tried the July Cronut (thry change the flavours every month) which was Hyuganatsu with Lime Sugar flavour. (A hyuganatsu is a type of Japanese citrus). It was delicious, as always, I really like this pastry but it's definitely not one you can eat a lot of since it's very rich. In any case they usually only sell 1 or 2 per customer. #cronut#dominiqueansel#ginza#dominiqueanselginza#hyuganatsu#julycronut#instafood#foodstagram#pastry#delicious#tokyofood#tokyo#東京#デザート#クロナッツ

s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886117874.26/warc/CC-MAIN-20170823055231-20170823075231-00262.warc.gz

CC-MAIN-2017-34

http://slidegur.com/doc/40060/particle-on-a-ring

math

Chemistry 2 Lecture 3 Particle on a ring approximation Learning outcomes from Lecture 2 •Be able to explain why confining a particle to a box leads to quantization of its energy levels • Be able to explain why the lowest energy of the particle in a box is not zero • Be able to apply the particle in a box approximation as a model for the electronic structure of a conjugated molecule (given equation for En). Assumed knowledge for today Be able to predict the number of π electrons and the presence of conjugation in a ring containing carbon and/or heteroatoms such as nitrogen and oxygen. The de Broglie Approach • The wavelength of the wave associated with a particle is related to its momentum: p = mv = h / λ • For a particle with only kinetic energy: E = ½ mv2 = p2 / 2m = h2 / 2mλ2 Particle-on-a-ring • Particle can be anywhere on ring • Ground state is motionless Particle-on-a-ring • Ground state is motionless • In higher levels, we must fit an integer number of waves around the ring 1 wave λ = 2πr 2 waves λ = 2πr/2 3 waves λ = 2πr/3 The Schrödinger equation • The total energy is extracted by the Hamiltonian operator. • These are the “observable” energy levels of a quantum particle Energy eigenfunction Hamiltonian operator Energy eigenvalue The Schrödinger equation • The Hamiltonian has parts corresponding to Kinetic Energy and Potential Energy. In terms of the angle θ: 2 2 ˆ H V ( 2mr 2 2 ) Potential Energy Hamiltonian operator Kinetic Energy “The particle on a ring” • The ring is a cyclic 1d potential E must fit an integer number of wavelengths 0 0 2p “The particle on a ring” p-system of benzene is like a bunch of electrons on a ring “The particle on a ring” • On the ring, V = 0. Off the ring V = ∞. sin j 2 2 ˆ H sin j 2 2 2mr 2 2 j 2mr 2 sin j j j = 1, 2, 3…. “The particle on a ring” • On the ring, V = 0. Off the ring V = ∞. cos j 2 2 ˆ H cos j 2 2 2mr 2 2 j 2mr 2 cos j j j = 0, 1, 2, 3…. Particle-on-a-ring • Ground state is motionless = constant “The particle on a ring” • The ring is a cyclic 1d potential E must fit an integer number of wavelengths 0 0 2p “The particle on a ring” j 2p j j 2 2 2m r mL 2 2 2 2 2 j = 0, 1, 2, 3…. length of circumference radius of ring j=3 j=2 j=1 j=0 “The particle on a ring” j=3 All singly degenerate Doubly degenerate above j=0 n=4 j=2 n=3 j=1 n=2 n=1 j=0 box ring Application: benzene Question: how many p-electrons in benzene? Answer: Looking at the structure, there are 6 carbon atoms which each contribute one electron each. Therefore, there are 6 electrons. benzene Question: what is the length over which the pelectrons are delocalized, if the average bond length is 1.40 Å? Answer: There are six bonds, which equates to 6 × 1.40 Å = 8.40 Å benzene Question: if the energy levels of the electrons are given by n = 2ℏ2j2p2/mL2, what is the energy of the HOMO in eV? Answer: since there are 6 p-electrons, and therefore the HOMO must have j=1. We know that L = 6 × 1.40 Å = 8.4 0Å. From these numbers, we get j = 3.41×10-19 j2 in Joules. The energy of the HOMO is thus 1 = 3.41×10-19J = 2.13 eV. j=3 j=2 j=1 j=0 benzene Question: what is the energy of the LUMO, and thus the HOMO-LUMO transition? j=3 Answer: j = 3.41×10-19 j2 in Joules. The energy of the LUMO is thus 2 = 1.365×10-18J = 8.52 eV. The energy of the HOMO-LUMO transition is thus 6.39 eV. j=2 j=1 j=0 benzene Question: how does the calculated value of the HOMO-LUMO transition compare to experiment? Answer: The calculated energy of the HOMO-LUMO transition is 6.39 eV. This corresponds to photons of wavelength l = hc/(6.39× 1.602×10-19) ~ 194 nm, which is not so far from the experimental value (around 200 nm). j=3 Hiraya and Shobatake, J. Chem. Phys. 94, 7700 (1991) j=2 j=1 j=0 Learning Outcomes • Be able to explain why confining a particle on a ring leads to quantization of its energy levels • Be able to explain why the lowest energy of the particle on a ring is zero • Be able to apply the particle on a ring approximation as a model for the electronic structure of a cyclic conjugated molecule (given equation for En). Next lecture • Quantitative molecular orbital theory for beginners Week 10 tutorials • Schrödinger equation and molecular orbitals for diatomic molecules Practice Questions 1. The particle on a ring has an infinite number of energy levels (since j = 0, 1,2, 3, 4, 5 …) whereas for a ring CnHn has only n p-orbitals and so n energy levels. C6H6, for example, only has levels with j = 3 (one level), j = 1 (two levels), j = 2 (two levels) and j = 3 (one level) (a) Using the analogy between the particle on a ring waves and the πorbitals on slide 17, draw the four π molecular orbitals for C4H4 and the six π molecular orbitals for C6H6 (b) Using qualitative arguments (based on the number of nodes and/or the number of in-phase or out-of-phase interactions between neighbours) construct energy level diagrams and label the orbitals as bonding, non-bonding or antibonding (c) Based on your answer to (b), why is C6H6 aromatic and C4H4 antiaromatic?

s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719136.58/warc/CC-MAIN-20161020183839-00061-ip-10-171-6-4.ec2.internal.warc.gz

CC-MAIN-2016-44

https://slideplayer.com/slide/5294551/

math

2 Learning ObjectivesUse the power conversion diagram to describe power flow for a three phase generator.Find line voltages and current for a Y-connected three phase generator. 3 Large AC generatorUnlike our generator model with a fixed magnetic field and rotating armature, it is more practical to fix the armature windings and rotate the magnetic field on large generators.Brushes and slip rings pass EXCITATION voltage to the field windings on the rotor to create the magnetic fieldMinimizes current flow through brushes to rotor windings3 4 DC Power Conversion Diagram ReviewDC Power Conversion DiagramElectricalMechanical 5 AC Generator power conversion diagram MechanicalElectricalPIN = Trotor=746*hpPOUTPelectr lossPmech lossNOTE: ω is the speed of the rotor, notthe angular velocity of the AC current. 6 Example Problem 1Consider a 3-phase, 4 pole, 60Hz, 450 V synchronous generator rated to supply kVA to a ship distribution system requiring a 0.8 lagging power factor.If this machine was operating at rated conditions, what would the real (P) and reactive (Q) power and the current being supplied?If the generator has an efficiency () of 95%, what torque does the prime mover provide?What is the speed of the rotor (rpm)? 7 Single-Phase Equivalent Circuit Just like 3-phase loads, it is useful to look at just a single phase of the generator.Einduced+EAN-XSRSNAIa Single-phase equivalent3-Phase Generator 8 Single-Phase Equivalent Circuit EAN is the phase voltage of the a-phase Ia is the line currentEinduced is the induced armature voltage.RS is the resistance of the generator’s stator coil.XS is the synchronous reactance of the stator coil.Einduced+EAN-XSRSNAIa 9 AC Generator Power Balance Mechanical Input Power can be calculated:Electrical (Armature) Losses can be calculated (notice 3 sets of armature windings, so must multiply by 3)Electrical output power can be calculatedThe total overall power balance: 10 Solution steps Determine the rms value of IL Determine phase angle of IL from the given power factor FP (using phase voltage as the reference) 11 Solution stepsDetermine Electrical losses (zero for a “negligible stator resistance”). This is PER-PHASE, so must multiply by 3 when adding to other power.Determine PINDetermine torque supplied to the generator if needed 12 Example Problem 2A submarine has a 3-phase, Y-connected, 2-pole, 60Hz synchronous generator rated to deliver kVA at a FP = 0.8 lagging with a line voltage of 450-V. The machine stator resistance RS = Ω. The synchronous reactance is Xs=0.08 Ω. The actual system load on the machine draws 900 kW at FP = 0.6 lagging. Assume that a voltage regulator has automatically adjusted the field current so that the terminal voltage is its rated value. Mechanical losses are 100 kW.Determine the reactive and apparent power delivered by the generator.Find the current delivered by the generatorWhat is the overall efficiency?The rated voltage (here, 450 V) is always a line voltage (this is the voltage we can measure between any two cables in a 3-phase system)

s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573827.2/warc/CC-MAIN-20190920030357-20190920052357-00462.warc.gz

CC-MAIN-2019-39

https://houstonarthurbweglein.com/math-solver-537

math

Factor a binomial We'll provide some tips to help you choose the best Factor a binomial for your needs. Math can be a challenging subject for many students. The Best Factor a binomial There are a lot of Factor a binomial that are available online. The best math experts are those who can teach math with clarity and ease. They have a good grasp of the subject matter and can explain it in an organized and insightful way. As well, they have the patience to work with students who might not be up to snuff when it comes to understanding certain concepts. Finally, they have a passion for the subject that shows in their teaching. Clearly, no two people are alike, so finding someone that you click with is key if you want your lessons to be memorable and effective. However, there are some qualities that all great math teachers should share. First and foremost is enthusiasm—it’s one of the most important factors in any lesson. You need to be engaged in order to make sure your students are too; otherwise, you’re just wasting your time. Next is patience—you need to be able to sit back, listen to what your students have to say, and take their feedback seriously. Lastly, you need to know the subject matter inside and out since this is one area where mistakes will happen more often than not. It is pretty simple to solve a geometric sequence. If we have a sequence A, B, C... of numbers and it looks like AB, then we can simply start at A and work our way down the list. Once we reach C, we are done. In this example, we can easily see AB = BC = AC ... Therefore once we reach C, the solution is complete. Let's try some other examples: A = 1, B = 2, C = 4 AB = BC = AC = ACB ACAB = ABC ==> ABC + AC ==> AC + AB ==> AC + B CABACCA ==> CA + AB ==> CA + B + A ==> CA + (B+A) ==> CABABABABABA The solutions are CABABABABABA and finally ABC. Trinomial factor or trinomial model is a statistical model that uses the coefficients of the three main terms in a formula. The coefficients describe the relationship between each variable in the formula and the function value (the dependent variable). Since there are three variables in a formula, it follows that each variable’s coefficient is expressed as a ratio. For example, if the coefficients for “age”, “x” and “y” are expressed as “a”:“b”:“c”, where “a” is the coefficient for “age” and “c” for “y”, then it can be inferred that humanity evolved at a rate of 1:1.25:0.25 = 0.61 = 1/3 per 1000 years. In statistics, a factor is an observation that represents one unit of an independent variable. A factor is often thought of as being observable; in other words, it is directly observable by an observer. However, a factor can also be unobservable (e.g., time-dependent); in this case, it can be thought of as being observable given certain assumptions about its underlying structure and behavior. Factors are sometimes referred to as determinants or causes. Factors can arise from the measured variable itself (e.g., In order to solve inequality equations, you have to first make sure that every variable is listed. This will ensure that you are accounting for all of the relevant information. Once you have accounted for all variables, you can start to solve the equation. When solving inequality equations, keep in mind that multiplication and division are not commutative operations. For example, if you want to find the value of x in an inequality equation, you should not just divide both sides by x. Instead, you should multiply both sides by the reciprocal of x: To solve inequality equations, it is best to use graphing calculators because they can handle more complex mathematics than simple hand-held calculators can. Graphing calculators can also be used to graph inequalities and other functions such as t and ln(x). If you have a good enough phone or camera, you can solve any problem with ease. It sometimes gets the picture wrong but, that can be fixed with the problem edit system. The app can even solve linear equations! Best and only calculator you will ever need! Five Stars! ***** Wonderful app for solving mathematics issues. It personally helped me a lot for solving my doubts. It was so helpful that I played for its pro version also, and I am not regretting for it. Now I am brilliant student in mathematics. 🎖🎖 I solve any kind of problem quickly. I refer everyone to download this and also pay for its pro version. 🤓

s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00525.warc.gz

CC-MAIN-2022-49

https://hasgeek.com/fossmeet-nitc/2016/sub/introduction-to-non-linear-functions-and-fractals-MTkgTyi2S1e1k4Hahkh1QP

math

Introduction to non linear functions and fractals The audience will understand how non linear functions work while modelling natural phenomena. It will then introduce fractals, how they’re generated and what they’re used for. Non linear functions are often used to model complex phenomena but they’re complex to analyse and their behaviour is close to impossible to predict. Dynamic systems (like the weather etc.) are often modelled using such equations. This talk will give the audience an idea of how complex even the simplest non linear system can be and how we can appreciate tools to analyse them. The talk will include several custom programs written specificially to illustrate ideas which are discussed. An interest in maths, a decent grasp of high school maths and some basic idea of computer graphics. I semi-regularly conduct workshops at The Lycaeum on various interesting technical topics. Chaos theory and fractals have been a hobby for a long time and I’ve been messing with this for over a decade now.

s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358074.14/warc/CC-MAIN-20211126224056-20211127014056-00135.warc.gz

CC-MAIN-2021-49

https://veteransvalorfund.com/general/kimtoya-and-sidney-are-participating-in-a-long-distance-bike-tour-the-rate-at-which-kimtoya-is-riding-is-represented-by-the-equation-y-12-5x-where-x-is-the-time-in-hours-and-y-is-the-total-distance-in-kilometers-the-rate-at-which-sidney-is-riding

math

Kimtoya and Sidney are participating in a long-distance bike tour.The rate at which Kimtoya is riding is represented by the equation y = 12.5x, where x is the time in hours and y is the total distance in kilometers.The rate at which Sidney is riding is represented by this table.Select answers from the drop-down menus to correctly complete the statements.Kimtoya rides at a rate of ____kilometers per hour and Sidney rides at a rate of ____kilometers per hour. Kimtoya's rate of speed is____Sidney's rate of speed. Time (h) Total distance (km) 2 25 3.5 43.75 5 62.5 On this problem, you just use the information you know and compare it. So... Kimtoya rides at a rate of 12.5 kilometers per hour and Sidney rides at a rate of 12.5 kilometers per hour. Kimtoya's rate of speed is equal to Sidney's rate of speed.

s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474686.54/warc/CC-MAIN-20240227184934-20240227214934-00476.warc.gz

CC-MAIN-2024-10

http://www.mathworksheetsworld.com/bytopic/irrationalnumbers.html

math

[advance to content] Click on the Irrational Numbers worksheet set you wish to view below. What are irrational numbers? Well, they aren't crazy. Although the word can mean not logical, in mathematics, the words irrational and rational have to do with ratios. To understand what an irrational number is, first you need to know what a rational number is. A rational number represents a quantity that can be written as a fraction. So, every 'normal' number (even 2 or 3 which can be written as 2/1 and 3/1) is rational, and all the fractions you can make with regular numbers are rational. At first glance, that definition seems to cover all the numbers. But there are quantities that cannot be written down as rational numbers (and no fraction would be equal to those quantities). These are called irrational and we use special symbols to represent them. How are irrational numbers used in the real world? Pi is an irrational number. The symbol for it is and it is pronounced the same as the word 'pie'. It appears in formulas for the area or circumference of a circle (and many other places). The area of a circle is equal to the radius times the radius times This is true for any circle and every circle. It's true when you want to make car tires, drill a hole, or figure out how much dough will be needed to make a round pizza. Pi is used in calculations with gears (circles!), wheels, pipes, coins...and pi is just one of an infinity of irrational numbers. A basic problem with irrational numbers. Because they cannot be written down as fractions, irrational numbers in practice are only used as approximations. An approximation for π is 3.14159. The 'real' quantity has been calculated to more than a trillion digits. But because the digits never end (nor repeat in any pattern) pi is shortened to a reasonable number of digits in actual use. This is the best solution when calculating the area of a circle or the volume of a sphere, just use enough digits to get the accuracy you need. This is what happens when you use an irrational number on your calculator. The square root button (√), when used with 2 gives an approximate answer, but one good enough for most calculations. Who discovered irrational numbers? The first proof of the existence of irrational numbers is credited to Hippasus around 500 BC. However, because they arise naturally from basic geometry, they were probably discovered much earlier. For instance, the area of a square is given as the length of one side times itself. Area = s x s. Suppose you have a square with an area = 2 and you want to find the length of the sides? Well, you need a number that, when multiplied by itself, equals 2. We express this number now as √2 (square root of two). This is an irrational number and cannot be written out - we use √2 as the symbol for it, just like π is a symbol and not a 'real' number. Anyone using the formulas in geometry will quickly discover these special numbers. An interesting fact about irrational numbers. Hippasus was a Pythagorean, a group that believed all numbers had to be rational. They felt this so strongly that when Hippasus proved irrationals existed, he was banished (or even killed, we aren't sure) for his forbidden knowledge. It's hard to believe now that people could have had such strong feelings about mathematics, but in Ancient Greece, these matters were tied into ideas about God and perfection, and Hippasus's discovery attacked these beliefs.

s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118310.2/warc/CC-MAIN-20170423031158-00428-ip-10-145-167-34.ec2.internal.warc.gz

CC-MAIN-2017-17

https://byjus.com/rs-aggarwal-solutions/rs-aggarwal-class-8-solutions-factorisation/

math

There are 3 cab companies A, B and C. They provide cab service at different time slots. The time taken for the trip depends upon the driver skill. The bar graph shown below gives the details. Suppose you have to reach your class as early as possible before 10 am. Which of the cabs will you choose and which time slot? Company A, C2, 9-10 Company B, C1, 8-9 Company C, C1, 8-9 Company C, C3, 10-11

s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743247.22/warc/CC-MAIN-20181116235534-20181117021534-00322.warc.gz

CC-MAIN-2018-47

http://www.insidecounsel.com/2010/05/24/morrison-on-metrics-legal-spendingthe-ins-and-outs?slreturn=1455104030

math

This column considers two common benchmarks and the statistical correlation between them: what legal departments spend internally divided by their number of lawyers and what they spend on outside counsel and other vendors, again divided by their number of lawyers. Typical figures for U.S. law departments come in at about $450,000 per lawyer inside and $600,000 per lawyer outside. Data from the General Counsel Metrics LLC study of global benchmarks lets us calculate the correlation between the two figures. In other words, when inside spend rises does outside spend also rise (both figures normalized per lawyer)? By how much?

s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701159155.63/warc/CC-MAIN-20160205193919-00279-ip-10-236-182-209.ec2.internal.warc.gz

CC-MAIN-2016-07

https://tavistocknursery.com/mastery-approach/essential-skills

math

Factorial of zero Best of all, Factorial of zero is free to use, so there's no sense not to give it a try! Math can be difficult for some students, but with the right tools, it can be conquered. The Best Factorial of zero Factorial of zero is a mathematical instrument that assists to solve math equations. How to solve by elimination is a method of problem solving where you systematically remove possible answers or solutions until only the correct answer is left. This can be useful when you are trying to narrow down a list of possibilities, such as when you are trying to find the culprit in a whodunit novel. To solve by elimination, you need to first identify all of the possible answers or solutions. Once you have a list, you can start to eliminate the ones that are not viable options. For example, if you were trying to figure out who stole a cookie from the cookie jar, and you had a list of suspects that included a cat, a dog, and a baby, you could eliminate the cat and the dog because they would not be able to reach thecookie jar. This would leave you with the baby as your only suspect. How to solve by elimination is a simple yet effective way to narrow down your options and find the right answer. How to solve for roots: There are several ways to solve for roots, or zeros, of a polynomial function. The most common method is factoring. To factor a polynomial, one expands it into the product of two linear factors. This can be done by grouping terms, by difference of squares, or by completing the square. If the polynomial cannot be factored, then one may use synthetic division to divide it by a linear term. Another method that may be used is graphing. Graphing can show where the function intersects the x-axis, known as the zeros of the function. Graphing can also give an approximate zero if graphed on a graphing calculator or computer software with accuracy parameters. Finally, numerical methods may be used to find precise zeros of a polynomial function. These include Newton's Method, the Bisection Method, and secant lines. Knowing how to solve for roots is important in solving many real-world problems. When we add two numbers together, we are simply combining two sets of objects into one larger set. The same goes for subtraction - when we take away one number from another, we are just separating two sets of objects. Multiplication and division work in a similar way. In multiplication, we are just adding a number to itself multiple times. And in division, we are just separating a number into smaller groups. So as you can see, basic mathematics is really not that complicated after all! How to solve logarithmic functions has been a mystery for many students. The concept seems difficult, but it is not as hard as it looks. There are three steps in solving logarithmic functions. First, identify the base of the logarithm. Second, use properties of logs to rewrite the equation. Third, solve for the unknown using basic algebra. These steps may seem confusing at first, but with practice they will become easy. With a little effort, anyone can learn how to solve logarithmic functions. Solving differential equations online can be a quick and easy way to get the answers you need. There are a variety of websites that offer this service, and most of them are free to use. All you need to do is enter the equation you want to solve and the website will do the rest. In addition, many of these websites also provide step-by-step solutions so you can see how the equation was solved. This can be a helpful way to learn how to solve differential equations on your own. Whether you're a student or a professional, solving differential equations online can save you time and effort. We cover all types of math problems This app is the best for calculator ever I try in the world, and I think even better then all facilities of online like google, WhatsApp, YouTube, almost every calculator apps etc and offline like school, calculator device etc (for calculator) It's a really helpful app. it’s so convenient it helped me a lot with my homework. you should definitely try this!! It's the basic reason I give these 5 stars Very good. All I could ask for is more detail with explaining the steps. Other than that, it's very good.

s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711150.61/warc/CC-MAIN-20221207053157-20221207083157-00740.warc.gz

CC-MAIN-2022-49

https://apps.uc.pt/courses/EN/unit/8649/745/2018-2019?type=ram&id=351

math

Real Analysis II, III; Linear Algebra and Analytic Geometry I, II. Active participation of the students in the theoretical and tutorial classes. This may include presentation in class of part of the homework assigments. Students' work is closely observed and frequently evaluated by the instructor. The student has access to the results of each evaluation and is encouraged to meet individually with the instructor to discuss his/her performance. A first contact with Integral Calculus of functions defined in Rn, culminating in the establishment of the four main Throrems of Integral Calculus: Central theorem of curvilinear integral,Riemann-Green Theorem, Stokes theorem and Gauss Theorem. The skills to be developed include learning the theoretical foundations of Integral Calculus in Rn; capacity of generalization and abstraction; capacity to pose problems and to translate them in mathematical language; calculation capacity; development of oral and written expression. 1. Elements of Jordan measure in Rn. 2. Double integral. Concept and properties. Fubini’s Theorem. Mean Value Theorem. Areas and Volumes. Surface area. Double integral in polar coordinates. 3. Triple integral. Concept and properties. Formulas of calculus. Triple integral in cylindrical and spherical coordinates. Applications.The concept of integral in Rn. 4. Curvilinear integral of a vector function. Concept and properties. Formulas of calculus. The concept of work. Curvilinear integral of a scalar function. Conservative vector fields. Independence of path. Riemann-Green Theorem. Necessary and sufficient conditions for a field to be conservative. Generalizations of Riemann-Green Theorem. 5. Change of variable in the double integral. 6. Surface integral. Stokes Theorem.Flux. 7. Gauss Theorem. 8. Gauss Theorem and conservation laws. Maria Paula Martins Serra de Oliveira Approval in this course unit requires to score at least 10 (out of 20). The students that perform, along the semester, the mid-term exams, the test, and/or the homework may be exempted from final examination. The sum of percentages corresponding to these three components is 100%. The other students are evaluated in a final exam which is worth 100%.: 100.0% J. E. Marsden, Elementary Classical Analysis. Freeman, NY, 1974. J. E. Marsden, Calculus III. 2nd edition. Springer, NY, 1991. M. P. Serra Oliveira, C. Oliveira, Análise Infinitesimal IV, Notas de Curso, 2008

s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578528058.3/warc/CC-MAIN-20190419201105-20190419223105-00551.warc.gz

CC-MAIN-2019-18

https://bejeweledquilts.blogspot.com/2016/07/update-on-my-personal-july-ufo-challeng.html

math

I am working in squares that are 8 x 8 which = 64 two and a half inch triangles. I need 4 of these 8 x 8 squares for the sides of my quilt which = 256 two and a half inch triangles plus 12 x 8 = 96 which added to the 256 = 352 two and a half inch triangles just for the two sides. I have that right now!!! Yea!!! Then for the top and bottom I need the same 256 plus 80 two and a half inch squares which = 336 this side is one 2 1/2" shorter than the other that is why there is a difference. I have that yea!!!! Now I am working on the end caps (that is what I am calling the end squares) I need two 8 x 8 which equals 128 which makes the total 2 1/2" squares that I need just for the border 806 two and a half inch squares I am not a mathematician and if my calculations are somewhat off.... No matter to me, I can add or take away but I know I will be close.... so no worries in that department Just giving you an idea of what I am up to I have a week left and I am determined. While calculating this I wanted to cry because I thought I almost had it but found an error in my figures (go figure) so back to the sewing machine.. You can cheer me on.... send a diet cherry limeaide send a paddy wagon!!!

s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247517815.83/warc/CC-MAIN-20190222114817-20190222140817-00388.warc.gz

CC-MAIN-2019-09

https://electronics.stackexchange.com/questions/14656/what-happens-to-my-led-when-i-supply-too-much-current?noredirect=1

math

I read somewhere that LEDs could self limit current up to a certain point and had a few lying around in my box so I decided to test this statement. Its true for roughly the voltage drop across the LED. But the question comes is what happened when I applied 20V to the LED? It made a loud popping sound. What happened to the internals of the LED? 8\$\begingroup\$ Um - They popped - blown, gone, killed.... \$\endgroup\$– Linker3000May 24, 2011 at 21:50 2\$\begingroup\$ I also noticed that my white LEDs went from white to blue and then to purple before they popped. @Linker3000 Define "popped", "blown", "gone", "killed". They are all different words with different meanings and each of the words has large number of meanings which are not related to process that occurred here. To me it looks like the question is about the physical process of LED destruction, which is very important to understand so that its early stages could be detected in a circuit that appears to be running fine. \$\endgroup\$– AndrejaKoMay 24, 2011 at 21:55 6\$\begingroup\$ You turned it into a DED, a Dark Emitting Diode. Although you might have gotten lucky and turned it into a SED, or Smoke Emitting Diode. \$\endgroup\$– user3624May 25, 2011 at 2:49 2\$\begingroup\$ You released the Magic Smoke! \$\endgroup\$– Connor WolfMay 26, 2011 at 23:32 1\$\begingroup\$ What happened was approximately the same thing that happened to a neon bulb I put accross 230 Vac as a kid at age 8, without the > 100k series resistor. It made a bang. Also, your parents might have been running towards your work bench, checking if you were still o.k. \$\endgroup\$– zebonautJun 3, 2011 at 22:40 Increasing heat from power dissipation causes a failure of the LED die. The change in colour, e.g. red and green LEDs going yellow at high currents, is probably because the die is actually glowing hot, i.e. near failure. Note that the red LED has a fall in wavelength, but the green one has an increase in wavelength. White LEDs going blue could be explained by the yellow-emitting phosphor in the LED being less effective at high currents. White LEDs are often constructed from a blue LED coated with a special phosphor which emits yellow light when blue light hits it creating a fairly even white light. So perhaps you are seeing more blue than the yellow phosphor can convert. 1\$\begingroup\$ Maybe the phosphor already died at that point. The orange/red glow is probably from heat alone. Once upon a time I had an EPROM glow red when I accidentally reversed the polarity of the power supply. \$\endgroup\$– starblueMay 25, 2011 at 19:28 An LED is a Light Emitting Diode. The key part of that name is "Diode." An LED is a diode. Diodes do not limit forward current very well. The extremely steep current/voltage curve (an exponential curve) is probably their second most important functional characteristic which results in sales of diodes. When you put a forward voltage on a diode (an LED, BE junction of a BJT, or whatever), it's current DOUBLES with each incremental 26mV of voltage. So if you applied 0.7V (700mV) and got 50mA, then you should get about 100mA at 726mV, 200mA at 752mV, 400mA at 778mV, and so on. So what would you expect at 20000mV? The theoretical answer is about 7 times 10 to the 222nd power amps. That is a '7' with about 222 zeros after it. But your home's circuit breaker (thankfully) limits current draw to something less than Quadra-Bazillions of times the total of all power plants on planet Earth. Your LED draws maybe 20 amps for a few microseconds, turning a very small volume inside it about as hot as the Sun, and then it is all over. If you do this with larger parts, the shrapnel can kill you. An electrian, at a factory I worked at, had the misfortune of crossing two phases of industrial strength AC with his screwdriver. As far as could be figured out, he was not electricuted: the plastic screwdriver handle protected him from that. However, the short instantly vaporized the metal in the screwdriver. The resulting explosion killed him. So provide external current limiting in line with your LED, or... wear safety goggles. EDIT: I got carried away with the point I was trying to make and erroneously said current doubles with each 25 mV across the diode junction. The actual factor is 'e', where 'e' = the base of the natural logarithm = about 2.7. So the current would increase by a factor of 2.7, not 2, for each 25mV. The damage to the device looks pretty much the same for large voltages, though.... \$\begingroup\$ A friend of a friend was working in a busbar cabinet, bolting down something with a spanner when he was startled by a spider - so he threw the spanner at it! As you said, the tool vaporized, but the resulting induction field twisted half the box off the wall. The engineer survived. No word on the spider. \$\endgroup\$ May 27, 2011 at 13:48 \$\begingroup\$ You are describing the Wikipedia topic Shockley diode equation. \$\endgroup\$ Jan 7, 2018 at 3:42 The weakest electrical portion of the LED fused. That part would vary based on LED construction. I've had this happen and blow off the tip of a 3mm LED with surprising energy, when I was young and messing with such questions. It hit the ceiling pretty hard.

s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945472.93/warc/CC-MAIN-20230326111045-20230326141045-00694.warc.gz

CC-MAIN-2023-14

https://www.assignmentexpert.com/homework-answers/chemistry/physical-chemistry/question-37169

math

Answer to Question #37169 in Physical Chemistry for Mohamme Shiraz A colourless compound weighing 0.84 on heating gives 0.22 g of CO2(carbon dioxide) and 0.09 g of H2O(water) and leaves a white residue.What is the molecular mass of the compound? Pls give the steps Calculate the amount of the released CO2 and H2O: n(CO2) = m/M = 0.22/44 = 0.005 mol; n(H2O) = m/M = 0.09/18 = 0.005 mol; The amount of substance of carbon dioxide is equal to the water amount, therefore we can assume that the amount of substance of initial compound is same. No we can calculate the molar mass: M = m/n = 0.84/0.005 = 168 g/mol.

s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347432521.57/warc/CC-MAIN-20200603081823-20200603111823-00422.warc.gz

CC-MAIN-2020-24

https://www.physicsforums.com/threads/grade-11-physics-need-help.648045/

math

1. The problem statement, all variables and given/known data Accelerating uniformly at a rate of 0.20m/s^2 from initial velocity of 3.0m/s, how long will it take to travel a distance of 12m 2. Relevant equations 3. The attempt at a solution Answer is 3.5 seconds But I don't know how you get that Also another question Chris accelerrates his massive SUV from rest at a rate of 4.0m/s^2 for 10s. he then travels at a constant velocity for 12s and finally comes to rest over a displacement of 100m. Determine his total displacement and average velocity, Answer is 780m;29m Please help!!!!

s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583514005.65/warc/CC-MAIN-20181021115035-20181021140535-00037.warc.gz

CC-MAIN-2018-43

https://123dok.org/article/imulink-description-description-siemens-vibration-control-routines-simulink.qmj55j18

math

Chapter 9: Description of Siemens LMS Vibration Control Routines in Simulink environment 9.2 S IMULINK MODEL DESCRIPTION The Simulink model represents the real “heart” of the control system. It is a very complex system in term of logic and implemented functions. It is composed by different blockset drowned at each level as Mux, Demux, MatLab embedded functions, switch and transfer functions and it is written in order to be an HIL closed loop system, capable to reproduce the same characteristics and behaviours of the test facility control system. The main control environment is endowed of appropriate “scopes” in order to see the output in real time. In Figure 51 and Figure 52 the Simulink environment at different levels is shown. How is possible to see, the control system shows different masks. They shadow control logic, but, going deeper, there are some function impossible to analyse in order to better understand the logic. In these terms, the Simulink model will be considered as a “black box” when the simulation run. pag. 88 Figure 51: Main control environment pag. 89 Figure 52: Detailed sine control environment pag. 90 However, from a system point of view, is possible to describe the qualitative way in which the control system operates. The code is able to perform the vibration control of a loaded system or device using up to 40 notchers (or DoFs) in order to monitoring their response. It is written in order to guarantee always 4 pilot curves. In fact, the original version of the model considered provide just one output coming from DEMUX. It is repeated considering 3 gain factors that amplifies the input signal. Subsequently, it becomes composed by 4 output. Then, is provided to the following MUX that recollect them with the other 40 signals coming from notchers in which some of them comes from the “C” matrix of the state space system and the remaining part from the “ground”. Figure 53 (a) Figure 53: Modification to the Simulink model: before (a), after (b) This implemented modelling strategy were tested with the reduced models mass- spring- damper described in “Chapter 8: The Virtual Shaker Testing approach (VST)” but is not appropriate in order to perform the VST using a condensed model in which the pilots are extracted with the Craig- Bampton theory, according to the location of the physical accelerometers attached to the vibration platform. For this reason, the Simulink model were modified in order to extract exactly 4 signals from DEMUX. Particularly, they refer to the pilots of the Craig- Bamption theory located into the first four position of the “C” matrix. Figure 53 (b). After that, the signals come into the real “sine controller” which, for each time step, perform actions as notching level calculation, control amplitude, time delay or sinusoidal input means cola. In Figure 54 is shown as is appear the mask of the sine control in which the input variables are recalled. One of the key points of the sine control are the control and estimation strategy. The first one represents the way in which the control takes place. It concerns the trend, and the values, of the pilots. Particularly, three possibilities are available: • Maximum: the control signal generates a control profile characterized by the maximum value of the pilots • Average: the control signal generates a control profile characterized by the sum of the pilot signals divided by the number of control channel, chosen in “Flow.m” • Minimum: the control signal generates a control profile characterized by the minimum value of the pilots The second one gives the way in which all the signals are evaluated. Basically, there are four possibilities: • Peak: it takes the greatest amplitude of the sample signal. If the system is characterized by noisy, this kind of evaluation could introduce some instabilities • Average: if the signal is characterized by “N” sample time, it calculates the average of the absolute value of them. It takes the complete signal. • RMS: it calculates the average of the squared values of “N” sample time during one period. As the average method, it evaluates the complete signal. It is able to produce a low drive signal • Harmonic: it is considered as the appropriate valuer for fundamental frequency research. It provides magnitude and phase response Figure 54: Sine control block parameters When the simulation starts, it requires the initial condition in order to join into the loop. They usually are the homogeneous conditions in which, using the formulation of a dynamic second order system, are displacement and speed equal to zeros. However, the block scheme implemented in Simulink is the “Discrete State Space”, shown in Figure 55. It come from the “Continuous State Space” system. In fact, how is described in “ pag. 92 Chapter 2: The State space systems”, this kind of mathematical formulation represent the best way in which to perform the control of a dynamic or electro-dynamic system. Particularly, the discrete formulation comes from the continuous quantizing the matrix operator with the "𝑡𝑠" sampling time consistent of the data acquisition system of the vibration facility. Nevertheless, from the algorithm point of view, it is able to solve the differential equation using the same procedure of the finite difference. Figure 55: Simulink block for Discrete State Space On the other hand, the code is not able to undergoes to modification in terms of solver. In fact, it is written usign a “discrete logic”, so is not possible to replace the “Conotinuous state space block” using the Runge-Kutta method. For sake of clarity, if Runge- Kutta is the exact approximation of a differential equation in time domain, the discrete state space solver is the approximation of this. In these term, the extracted curves using the discrete method will match in some points with them extrated using the continuous method. When the simulation advance up to the maximum value of the frequency (typically 100 Hz for sine sweep) the Simulink model send out two matrix: “spectra.mat” and “spectra_notch.mat” in which are recollect the requested output and classified by columns in term of time, frequency related notcher values and control profiles. The output that is possible to extract to the sine control system are: • 4 pilot curves: they describe the variation in time domain of the considered pilot. How we said before, talking in terms of signals, is necessary to guarantee 4 signals to the control system. They could be overlapped or not • Up to 40 notched curves in frequency and time domain • The control signal profile compared to the abort and alarm limits • Two “on/off diagram” in which are shown if one, or more Dofs are notched and which of them • The drive amplitude of the input • The cola: it shows the sinusoidal input imposed to the coil • The enhancement of the frequency during the simulation Particularly, the control curve (i.e. the acceleration of the pilots handles by one of the controls and strategy criteria) is compared to the upper and lower abort and alarm limit. pag. 93 Usually, during a vibration test if the control curve exceeds one of the two abort limit (±6 dB) it is interrupted. However, into the LMS vibration control environment we are to see the control curve during all the simulation span, in frequency or time domain, even if it exceeds the upper or the lower value. Probably, in fact, the aim of do not interrupt the running simulation is to permit to the engineer to observe where and when the control “burst” or “disappears”. This, in order to apply the required modification to the control environment in terms of compression factor, notch profile, control strategy or damping model if the FEM model is unprovided. In this way, the sine control lives in a wide set of simulation distinguished by the possible variation of each control parameter and under a precise strategy to distinguish the type of control. Obviously, the final result of the VST activity is to suggest the more appropriate value at each control parameter, before the real vibration test into the facility centre, in order to observe some specified behaviours during the base excitation and guarantee that them do not provoke any rupture. For these reason does not exist a unique and unequivocal result, but it depends on what the test facility engineers want to observe. In these terms, the VST shall emanate a variety of output, based on what they want.

s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943695.23/warc/CC-MAIN-20230321095704-20230321125704-00703.warc.gz

CC-MAIN-2023-14

https://mathequitytask.com/about/

math

An equity task is an activity that makes mathematical instruction more equitable by improving: - Rigor (“I do rigorous math”): Students use clear and precise mathematical language while engaging in challenging mathematical content that extends their understanding. - Diversity (“I do math in different ways”): Students analyze different approaches and cultural contributions to mathematics. - Identity (“I believe I can do math”): Students believe they can excel in mathematics by supporting each other while refining mathematical ideas and explaining how mathematics relates to their lives. - Justice (“I do math to improve my community”): Students use mathematics to recommend actions that make their communities fairer. We developed a rubric for measuring each of the four components of an equity task. We describe how we developed the idea of equity tasks in a 2023 Edutopia article called “Incorporating Equity Tasks into Everyday Math Instruction.” This site is maintained by Bobson Wong and Larisa Bukalov. See our complete list of equity tasks.

s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816853.44/warc/CC-MAIN-20240413211215-20240414001215-00436.warc.gz

CC-MAIN-2024-18

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&tp=&arnumber=5680973&contentType=Journals+%26+Magazines&sortType%3Dasc_p_Sequence%26filter%3DAND(p_IS_Number%3A5721294)

math

Skip to Main Content In this paper, we study the distribution of attraction basins of multiple equilibrium points of cellular neural networks (CNNs). Under several conditions, the boundaries of the attracting basins of the stable equilibria of a completely stable CNN system are composed of the closures of the stable manifolds of unstable equilibria of (n - 1) dimensions. As demonstrations of this idea, under the conditions proposed in the literature which depicts stable and unstable equilibria, we identify the attraction basin of each stable equilibrium of which the boundary is composed of the stable manifolds of the unstable equilibria precisely. We also investigate the attracting basins of a simple class of symmetric 1-D CNNs via identifying the unstable equilibria of which the stable manifold is (n - 1) dimensional and the completely stable asymmetric CNNs with stable equilibria less than 2n.

s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469258943366.87/warc/CC-MAIN-20160723072903-00204-ip-10-185-27-174.ec2.internal.warc.gz

CC-MAIN-2016-30

https://aic-components.com/power-equipment/question-what-is-difference-between-translation-and-transformation.html

math

Is a translation a transformation? A translation (or “slide”) is one type of transformation. In a translation, each point in a figure moves the same distance in the same direction. Example: … If each point in a triangle moves 3 units to the left, and there is no up or down movement, then that is also a translation! What is difference between transformation and transformation? You use a transform to perform a transformation. That is, if you’re outlining the model of which you speak it would be “transform”. However, if you’re referring to the actual effect (in runtime, so to speak), its transformation. In my opinion, it is more convenient to use “transformation”. What is the difference between translation and transformation in Cucm? Translation patterns follow the same general rules and use the same wildcards as route patterns. As with route patterns, translation patterns are assigned to a partition. … Transformation patterns are configured when the calling or called number needs to be changed before the system sends it to the phone or the PSTN. How do you describe translation? A translation is a type of transformation that moves each point in a figure the same distance in the same direction. … You can describe a translation using words like “moved up 3 and over 5 to the left” or with notation. What does the word transformed mean? Verb. transform, metamorphose, transmute, convert, transmogrify, transfigure mean to change a thing into a different thing. transform implies a major change in form, nature, or function. What is a transform in unity? In Unity, the Transform component has three visible properties – the position, rotation, and scale. … Means, Transform is used to determine the Position, Rotation, and Scale of each object in the scene. Every GameObject has a Transform. What is transform in unity C#? Every object in a Scene has a Transform. It’s used to store and manipulate the position, rotation and scale of the object. Every Transform can have a parent, which allows you to apply position, rotation and scale hierarchically. This is the hierarchy seen in the Hierarchy pane. What is an example of transformation? Transformation is the process of changing. An example of a transformation is a caterpillar turning into a butterfly. What is the translation formula? A translation is a function that moves every point a constant distance in a specified direction. A vertical translation is generally given by the equation y=f(x)+b y = f ( x ) + b .

s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573193.35/warc/CC-MAIN-20220818094131-20220818124131-00285.warc.gz

CC-MAIN-2022-33

https://www.groundai.com/project/emergent-universe-scenario-bouncing-and-cyclic-universes-in-degenerate-massive-gravity/

math

Emergent Universe Scenario, Bouncing and Cyclic Universes in Degenerate Massive Gravity Shou-Long Li, H. Lü, Hao Wei, Puxun Wu and Hongwei Yu Department of Physics and Synergetic Innovation Center for Quantum Effect and Applications, Hunan Normal University, Changsha 410081, China School of Physics, Beijing Institute of Technology, Beijing 100081, China Center for Joint Quantum Studies, School of Science, Tianjin University, Tianjin 300350, China We consider alternative inflationary cosmologies in massive gravity with degenerate reference metrics and study the feasibilities of the emergent universe scenario, bouncing and cyclic universes. We focus on the construction of the Einstein static universe, classes of exact solutions of bouncing and cyclic universes in degenerate massive gravity. We further study the stabilities of the Einstein static universe against both homogeneous and inhomogeneous scalar perturbations and give the parameters region for a stable Einstein static universe. firstname.lastname@example.org email@example.com firstname.lastname@example.org email@example.com firstname.lastname@example.org General relativity (GR), as a classical theory describing the non-linear gravitational interaction of massless spin-2 fields, is widely accepted at low energy limit. Nevertheless, there are still several motivations to modify GR, based on both theoretical considerations (e.g. [1, 2]) and observations (e.g.[3, 4].) One proposal, initiated by Fierz and Pauli , is to assume that the mass of graviton is nonzero. Unfortunately, the interactions for massive spin-2 fields in Fierz-Pauli massive gravity have long been thought to give rise to ghost instabilities . Recently, the problem has been resolved by de Rham, Gabadadze and Tolley (dRGT) , and dRGT massive gravity has attracted great attention and is studied in various areas such as cosmology [7, 8, 9, 10] and black holes [11, 12]. We refer to e.g. [13, 14, 15] and reference therein for a comprehensive introduction of massive gravity. There are several extensions of dRGT massive gravity for different physical motivations, such as bi-gravity , multi-gravity , minimal massive gravity , mass-varying massive gravity , degenerate massive gravity and so on . Thereinto, the degenerate massive gravity was initially proposed by Vegh to study holographically a class of strongly interacting quantum field theories with broken translational symmetry. Later this theory has been studied widely in the holographic framework [22, 23, 24, 25] and black hole physics [26, 27, 28, 29, 30]. However, the cosmological application of this theory is few. Recently, together with suitable cubic Einstein-Riemann gravities and some other matter fields, degenerate massive gravity was used to construct exact cosmological time crystals with two jumping points, which provides a new mechanism of spontaneous time translational symmetry breaking to realize the bouncing and cyclic universes that avoid the initial spacetime singularity. It is worth noting that the higher derivative gravities are indispensable for the realization of cosmological time crystals. However, if we consider only the infrared modification of GR, we can study instead the feasibilities of bouncing and cyclic models in degenerate massive gravity without the higher-order curvature invariants. Actually, it is valuable to investigate alternative inflationary cosmological models within the standard big bang framework, because traditional inflationary cosmology [32, 33, 34, 35] suffers from both initial singularity problem and trans-Planckian problem . By introducing a mechanism for a bounce in cosmological evolution, both the trans-Planckian problem and initial singularity can be avoided. The bouncing scenario can be constructed via many approaches such as matter bounce scenario , pre-big-bang model , ekpyrotic model , string gas cosmology , cosmological time crystals and so on [42, 43, 44]. The cyclic universe, e.g. , can be viewed as the extension of the bouncing universe since it brings some new insight into the original observable universe . Another direct solution to the initial singularity proposed by Ellis et al. [47, 48], i.e., emergent universe scenario, is assuming that the universe inflates from a static beginning, i.e., the Einstein static universe, and reheats in the usual way. In this scenario, the initial universe has a finite size and some past-eternal inflation, and then evolves to an inflationary era in the standard way. Both horizon problem and the initial singularity are absent due to the initial static state. Actually, these alternative inflationary cosmologies have been studied in different class of massive gravities. The bouncing and cyclic universes have been studied in mass-varying massive gravity . The emergent scenario has been also studied in dRGT massive gravity [50, 51] and bi-gravity [52, 53]. To our knowledge, these alternative inflationary models have not been studied in degenerate massive gravity. For our purpose, we would like to study the feasibilities of emergent universe, bouncing and cyclic universes in massive gravity with degenerate reference metrics. The remaining part of this paper is organized as follows. In Sec. 2, we give a brief review of the massive gravity and its equations of motion. In Sec. 3, we study the emergent universe in degenerate massive gravity with perfect fluid. First we obtain the exact Einstein static universe solutions in sevaral cases. Then we give the linearized equations of motion and discuss the stabilities against both homogeneous and inhomogeneous scalar perturbations. We give the parameters regions of stable Einstein static universes. In Sec. 4, we construct exact solutions of the bouncing and cyclic universes in degenerate massive gravity with a cosmological constant and axions. We conclude our paper in Sec. 5. 2 Massive gravity In this section, following e.g. , we briefly review massive gravity. The four dimensional action of massive gravity is given by where is Plank mass and we assume in the rest discussion, is the action of matters, is the Ricci scalar, represents the determinant of , represents the mass of graviton, are free parameters and are interaction potentials which can be expressed as follows, where the regular brackets denote traces, such as . is given by where is a fixed symmetric tensor and called reference metric, which is given by where is the Minkowski background and are the Stückelberg fields introduced to restore diffeomorphism invariance . In the limit of , massive gravity reduces to GR. The equations of motion are given by Generally, all the Stückelberg fields are nonzero in massive gravity and the rank of the matrix (2.5) is full, i.e. . In Ref. , there are two spatial nonzero Stückelberg fields which break the general covariance in massive gravity. The matrix has rank 2 thus being degenerate. The massive gravity with degenerate reference metrics is called degenerate massive gravity. For our purpose, we set only the temporal Stückelberg field to equal to zero. It follows that massive gravity we consider in this paper has degenerate reference metrics of rank 3. And the unitary gauge of the corresponding Stückelberg fields is defined simply by . So are given by in the basis , where is a positive constant. 3 Emergent universe scenario In this section, we consider the realization of emergent universe scenario in the context of degenerate massive gravity. We consider only spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) metric because the Stückelberg fields in degenerate massive gravity are chosen in a spatially flat basis. On the other hand, based on the latest astronomical observations [55, 56], the universe is at good consistency with the standard spatially-flat case. In the following discussion, we assume that the matter field is composed of perfect fluids. Firstly we construct the Einstein static universe in several cases. Then we study the stability against both homogeneous and inhomogeneous scalar perturbations. 3.1 Einstein static universe The spatially flat FLRW metric is given by The energy-momentum tensor corresponding to perfect fluids is given by where and represent the energy density and pressure respectively, is the constant equation-of-state (EOS) parameter, and velocity 4-vector is given by where dot denotes the derivative with respect to time. For the sake of obtaining the Einstein static universe, we let scale factor and . We request to avoid the ghost excitation from massive gravity. The energy density can be solved from the Friedmann equation (3.4), The Einstein static universe solution is given by . Because there are several parameters in the Eq. (3.8), we will discuss them in different cases. 3.1.1 Case 1: , , In this case, Eq. (3.8) reduces to a simple linear equation. The Einstein static solution is given by Case (1.1): For the solution is given by Case (1.2): For , the solution is given by 3.1.2 Case 2: , In this case, Eq. (3.8) reduces to a quadratic equation. The Einstein static solutions are given by Case (2.1): For , and the solution is given by Case (2.2): For , and the solution is given by The existence of requires the following two cases: Case (2.3): For , and the solution is given by Case (2.4): For , and the solution is given by 3.1.3 Case 3: In this case, Eq. (3.8) can be rewritten as For and , there are three real solutions which are given by For and , there is one real solution which is given by For , there is one real solution which is given by For , there is one real solution which is given by There are three free parameters and in the solutions. It is hard to analyze the parameters region of existence of all six solutions analytically. Instead we analyze the existence regions numerically and plot the parameters regions of the existence of all solutions in Fig. 1. We find that the solutions and cannot exist. In the previous subsection, we study the existence of the Einstein static universe in massive gravity with degenerate reference metrics. However, the emergent scenario does not thoroughly solve the issue of big bang singularity when perturbations are considered. For example, although the Einstein static universe is stable against small inhomogeneous perturbations in some cases [57, 58, 59, 60], the instability exists in previous parameters range against homogeneous perturbations . So it is valuable to explore the viable Einstein static universe by considering both homogeneous and inhomogeneous scalar perturbations. Actually, the stabilities of the Einstein static universe has been studied in various modified gravities, for examples, loop quantum cosmology , theory [63, 65, 64], theory [66, 67], modified Gauss-Bonnet gravity [68, 69], Brans-Dicke theory [70, 71, 72, 73], Horava-Lifshitz theory [74, 75, 76], brane world scenario [77, 78, 79], Einstein-Cartan theory , gravity , Eddingtong-inspired Born-Infeld theory , Horndeski theory [83, 84], hybrid metric-Palatini gravity and so on [86, 87, 88, 89, 90, 91, 92]. We refer to e.g. and reference therein for more details of stability of the Einstein static universe. In the following discussions, we would consider the stabilities of the Einstein static universe against both homogeneous and inhomogeneous scalar perturbations in degenerate massive gravity. 3.2.1 Linearized Massive Gravity Now we study the linear massive gravity with degenerate reference metrics. We use the symbols bar and tilde representing the background and the perturbation components of the metric respectively. First, we obtain the linearized equations of motion The perturbed metric can be written as where is the background metric which is given by Eq. (3.1) with and is a small perturbation. For our purpose, we consider scalar perturbations in the Newtonian gauge. is given by where and are functions of . For scalar perturbations, it is useful to perform a harmonic decomposition , Now the indexes are lowered and raised by the background metric unless otherwise stated. By using the relation , the inverse metric is perturbed by So the perturbed can also be written as According to Eq. (2.4), we have , i.e., So we have where “ 0 ” and “ ” denote time and space components respectively and the same index does not mean the Einstein rule. For perfect fluids, the perturbations of energy density and pressure are and respectively. The perturbations of velocity are given by where and are also functions of . The perturbed energy momentum tensor is given by It is useful to perform a harmonic decomposition of , In these expressions, summation over co-moving wavenumber are implied. The harmonic function satisfies where is Laplacian operator and is separation constant. For spatially flat universe, we have where the modes are discrete [60, 69]. Substituting Eqs. (3.30) and (3.42) into (3.37), after some algebra, we find where satisfies a second order ordinary differential equation To analyse the stabilities of the Einstein static universe in massive gravity with a degenerate reference metric, we require the condition of existence of the oscillating solution of Eq. (3.45) which is given by In the following discussions, we study the parameters region satisfying reality conditions (3.6) and (3.7), and stability condition (3.47) for the Einstein static flat universes against both homogeneous and inhomogeneous perturbations in different cases. 3.2.2 Case 1: , , The stabilities of the Einstein static universe (3.11) require

s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703538741.56/warc/CC-MAIN-20210123222657-20210124012657-00283.warc.gz

CC-MAIN-2021-04

http://gfy.com/showthread.php?t=1070932

math

|06-10-2012, 03:39 AM||#1| Join Date: Apr 2003 $$$$$$$ Looking for DATING / WEBCAM / SWINGERS Links - Top Prices Paid $$$$$$$ As per the thread title I'm looking for dating, webcam or swingers links, not really interested in any porn sites per se. Please email me: tim AT timwhale DOT com with: If you've got blogs I really want blog posts, please also include a price per post.

s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368710115542/warc/CC-MAIN-20130516131515-00096-ip-10-60-113-184.ec2.internal.warc.gz

CC-MAIN-2013-20

https://www.docsity.com/en/users/profile/tomcrawford/

math

A rectangular airstrip measures 32.30 m by 210 m, with the width measured more accurately than the length. Find the area, taking into account significant figures. (a) 6.783 0 3 103 m2 (b) 6.783 3 103 m2 (c) 6.78 3 103 m2 (d) 6.8 3 103 m2 (e) 7 3 103 m2 "Races are timed to an accuracy in given seconds. What distance could a person in-line skating at given speed travel in that period of time? " Races are timed to an accuracy of 1/1 000 of a second. What distance could a person in-line skating at a speed of 8.5 m/s travel in that period of... The quantities which have magnitude or size & direction, associated with them are vector quantities "In the event san francisco spa the other way possible regarding fixing a problem, the other might imagine of more than onealgorithm for similar diffi... "Commercial floppy disks were first manufactured in the early 1970s, when they measured a full eight inches across; by the end of the decade these beh...

s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267162385.83/warc/CC-MAIN-20180925182856-20180925203256-00496.warc.gz

CC-MAIN-2018-39

https://www.coursehero.com/file/5955444/31-pdfsam-apluspreptt1pkg/

math

5. Infections with Aphtoviruses, which are the cause of hand-foot-and-mouth disease in tropics, can be prevented by formalin-inactivated vaccine Select the best answer: A. None of the above B. 1, 2, 3 C. 1, 4 D. 3 E. 3, 5 11. Which statement(s) is/are true about isolation and purification of viruses? 1. The magnitude of the centrifugal force is proportional to the molecular weight of viruses, angular velocity, and the square of the radial distance from axis of rotation to viral particles 2. If two viruses, one with spherical shape and the other with rod-shape, have the same molecular weight, the spherical virus will have the lower sedimentation coefficient 3. If Tobacco Mosaic Virus (TMV) consists of 95% protein and 5% RNA, and if Brome Mosaic Virus (BMV) consists of 80% protein and 20% RNA, then BMV sediments in the upper layer and TMV sediments in the lower layer in Equilibrium Centrifugation 4. If the sedimentation coefficient (S) is 160S for Polioviruses and 80S for BMV, This is the end of the preview. access the rest of the document. best answer, BMV, Polioviruses, BMV sediments, Cauliflower Mosaic Viruses

s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257651820.82/warc/CC-MAIN-20180325044627-20180325064627-00751.warc.gz

CC-MAIN-2018-13

http://bizfinance.about.com/od/financialratios/f/finratioanal3.htm

math

The current ratio is probably the best known and most often used of the liquidity ratios. Liquidity ratios are used to evaluate the firm's ability to pay its short-term debt obligations such as accounts payable (payments to suppliers) and accrued taxes and wages. Short-term notes payable to a bank, for example, may also be relevant. On the balance sheet, the current portions of the document are assets and liabilities that convert to cash within one year. Current assets and current liabilities make up the current ratio. Calculation of the Current Ratio The current ratio is calculated from balance sheet data as Current Assets/Current Liabilities. So, if a business firm has $200 in current assets and $100 in current liabilities, the calculation is $200/$100 = 2.00X. The "X" (times) part at the end is important. It means that the firm can pay its current liabilities from its current assets two times over. Intrepretation and Current Ratio Analysis This is obviously a good position for the firm to be in. It can meet its short-term debt obligations with no stress. If the current ratio was less than 1.00X, then the firm would have a problem meeting its bills. So, usually, a higher current ratio is better than a lower current ratio with regard to maintaining liquidity. For more analysis of the current ratio, see Lesson 2 of the e-course Financial Analysis Using 13 Financial Ratios

s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510267729.10/warc/CC-MAIN-20140728011747-00004-ip-10-146-231-18.ec2.internal.warc.gz

CC-MAIN-2014-23

https://www.solutioninn.com/study-help/process-dynamics-control/a-process-control-system-contains-the-following-transfer-functionsa-show

math

A process control system contains the following transfer functions: (a) Show how G O L (s) can be approximated by (a) Show how GOL (s) can be approximated by a FOPTD model; Find K,Ï, and θ for the open-loop process transfer function. (b) Use direct substitution and your FOPTD model to find the range of Kc values that will yield a stable closed-loop system. Check your value of Kcm for the full-order model using simulation. This problem has been solved! Step by Step Answer:

s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100112.41/warc/CC-MAIN-20231129141108-20231129171108-00102.warc.gz

CC-MAIN-2023-50